---------------------------------------------------------------------------------
      name:  <unnamed>
       log:  /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/
> JEPSReplicationfiles/Appendix/appendixreplication_v2.log
  log type:  text
 opened on:  27 May 2022, 13:29:47

. use "${main_data}/pol_v0.8.dta", clear
(Merges randomization data with pol_v0.5)

. 
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Nested Quotas
. * Table A1-A6 report the planned and actual sample sizes of different demograph
> ics. The code below shows the actual sample sizes in the data.
. *Table A1
. tab vote2016

           2016 |
   presidential |
  election vote |
       decision |      Freq.     Percent        Cum.
----------------+-----------------------------------
          Trump |        938       30.75       30.75
        Clinton |        978       32.07       62.82
Other candidate |        149        4.89       67.70
        No vote |        861       28.23       95.93
        Not say |        107        3.51       99.44
          Other |         17        0.56      100.00
----------------+-----------------------------------
          Total |      3,050      100.00

. 
. *Table A2
. tab race

           Race of |
       participant |      Freq.     Percent        Cum.
-------------------+-----------------------------------
Non-hispanic white |      2,126       69.70       69.70
Non-hispanic black |        163        5.34       75.05
          Hispanic |        492       16.13       91.18
             Asian |        147        4.82       96.00
   American Indian |         14        0.46       96.46
            Others |         73        2.39       98.85
 Prefer not to say |         35        1.15      100.00
-------------------+-----------------------------------
             Total |      3,050      100.00

. 
. *Table A3
. tab edu if race==1  /*race is 1 for non-hispanic white*/

Education of participant |      Freq.     Percent        Cum.
-------------------------+-----------------------------------
Not complete high school |         70        3.29        3.29
        High school grad |        584       27.47       30.76
            Some college |        539       25.35       56.11
            College grad |        571       26.86       82.97
               Post grad |        353       16.60       99.58
                   Other |          9        0.42      100.00
-------------------------+-----------------------------------
                   Total |      2,126      100.00

. 
. *Table A4
. tab edu if race==2 /*race is 2 for non-hispanic blacks*/

Education of participant |      Freq.     Percent        Cum.
-------------------------+-----------------------------------
Not complete high school |          7        4.29        4.29
        High school grad |         42       25.77       30.06
            Some college |         38       23.31       53.37
            College grad |         50       30.67       84.05
               Post grad |         26       15.95      100.00
-------------------------+-----------------------------------
                   Total |        163      100.00

. 
. *Table A5
. tab edu if race==3  /*race is 3 for hispanic*/

Education of participant |      Freq.     Percent        Cum.
-------------------------+-----------------------------------
Not complete high school |         26        5.28        5.28
        High school grad |        164       33.33       38.62
            Some college |        125       25.41       64.02
            College grad |        125       25.41       89.43
               Post grad |         46        9.35       98.78
                   Other |          6        1.22      100.00
-------------------------+-----------------------------------
                   Total |        492      100.00

. 
. *Table A6
. tab edu if race==4 /*race is 4 for asian*/

Education of participant |      Freq.     Percent        Cum.
-------------------------+-----------------------------------
Not complete high school |          3        2.04        2.04
        High school grad |         15       10.20       12.24
            Some college |         29       19.73       31.97
            College grad |         57       38.78       70.75
               Post grad |         43       29.25      100.00
-------------------------+-----------------------------------
                   Total |        147      100.00

. *------------------------------------------------------------------------------
> -
. 
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Descriptive Statistics
. * Table A7
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * Table A7: Participant Characteristics ******
. *------------------------------------------------------------------------------
> -
. * OUTCOME
. * Correct(%)
. gen pct_correct = correct * 100

. label var  pct_correct "Correct answer(\%)"

. 
. * TREAETMENTS AND THEORETICAL VARIABLES
. * Covid-Increase treatment(%)
. gen pct_covid_inc = covid_inc * 100

. label var  pct_covid_inc "Covid-Increase treatment(\%)"

. 
. * Covid-Decrease treatment(%)
. gen pct_covid_dec = covid_dec * 100

. label var  pct_covid_dec "Covid-Decrease treatment(\%)"

. 
. * Numeracy
. label var  num "No. of correct answer (out of 6)"

. 
. * Numeracy standardized
. label var  numeracy "Numeracy (standardized: -2.70 to 3.30, centered at 0)"

. 
. 
. * Incentive(%)
. gen pct_incentive = incentive * 100

. label var  pct_incentive "Incentive(\%)"

. 
. * Conservative
. label var nonstd_conservative "Conservative (-3 to 3)"

. 
. * Conservative standardzied
. label var conservative "Conservative (standardized: -1.73 to 1.88, centered at 
> 0)"

. 
. * Congenial
. label var       congenial "Congenial"

. 
. * CONTROLS
. * Age
. label var  age "Age"

. 
. * Gender - Female(%)
. gen pct_female = female * 100
(14 missing values generated)

. label var  pct_female "Female(\%)"

. 
. * Ethnicity - Non-Hispanic White(%)
. gen race_nhw = 0

. replace race_nhw = 1 if race == 1
(2,126 real changes made)

. label variable race_nhw "=1 if race is Non-Hispanic White"

. gen pct_race_nhw = race_nhw * 100

. label var  pct_race_nhw "Non-hispanic white(\%)"

. 
. * Ethnicity - Hispanic(%)
. gen race_hispanic = 0

. replace race_hispanic = 1 if race == 3
(492 real changes made)

. label variable race_hispanic "=1 if race is Hispanic"

. gen pct_race_hispanic = race_hispanic * 100

. label var  pct_race_hispanic "Hispanic(\%)"

. 
. * Ethnicity - Others(%)
. gen race_other = 0

. replace race_other = 1 if race != 1 & race != 3
(432 real changes made)

. label variable race_other "=1 if race is Other"

. gen pct_race_other = race_other * 100

. label var  pct_race_other "Other races(\%)"

. 
. * Education - High school or less(%)
. gen edu_highschool = 0

. replace edu_highschool = 1 if edu == 1 | edu == 2
(956 real changes made)

. label variable edu_highschool "=1 if edu is high school or less"

. gen pct_edu_highschool = edu_highschool * 100

. label var  pct_edu_highschool "High school or less(\%)"

. 
. * Education - College grad/Some college(%)
. gen edu_college = 0

. replace edu_college = 1 if edu == 3 | edu == 4
(1,586 real changes made)

. label variable edu_college "=1 if edu is college grad or some college"

. gen pct_edu_college = edu_college * 100

. label var  pct_edu_college "College grad/Some college(\%)"

. 
. * Education - Post grad/others(%)
. gen edu_other = 0

. replace edu_other = 1 if edu == 5 | edu == 6
(508 real changes made)

. label variable edu_other "=1 if edu is post grad or others"

. gen pct_edu_other = edu_other * 100

. label var  pct_edu_other "Post grad/Others(\%)"

. 
. * Vote2016 - Donald Trump(%)
. gen vote2016_trump = 0

. replace vote2016_trump = 1 if vote2016 == 1
(938 real changes made)

. label variable vote2016_trump "=1 if vote2016 is Trump"

. gen pct_vote2016_trump = vote2016_trump * 100

. label var  pct_vote2016_trump "Vote Donald Trump(\%)"

. 
. * Vote2016 - Hillary Clinton(%)
. gen vote2016_clinton = 0

. replace vote2016_clinton = 1 if vote2016 == 2
(978 real changes made)

. label variable vote2016_clinton "=1 if vote2016 is Clinton"

. gen pct_vote2016_clinton = vote2016_clinton * 100

. label var  pct_vote2016_clinton "Vote Hillary Clinton(\%)"

. 
. * Vote2016 - No vote(%)
. gen vote2016_novote = 0

. replace vote2016_novote = 1 if vote2016 == 4
(861 real changes made)

. label variable vote2016_novote "=1 if vote2016 is No vote"

. gen pct_vote2016_novote = vote2016_novote * 100

. label var  pct_vote2016_novote "No Vote(\%)"

. 
. 
. estpost sum             pct_correct                                            
>                                                          ///
>                                 pct_covid_inc pct_covid_dec num numeracy pct_in
> centive                                  ///
>                                 nonstd_conservative conservative congenial     
>                                                                  ///
>                                 age pct_female pct_race_nhw pct_race_hispanic p
> ct_race_other    ///
>                                 pct_edu_highschool pct_edu_college pct_edu_othe
> r                                ///
>                                 pct_vote2016_trump pct_vote2016_clinton pct_vot
> e2016_novote             

             |  e(count)   e(sum_w)    e(mean)     e(Var)      e(sd)     e(min) 
-------------+------------------------------------------------------------------
 pct_correct |      3050       3050   42.22951    2440.42    49.4006          0 
pct_covid~nc |      3050       3050   50.68852   2500.346   50.00346          0 
pct_covid~ec |      3050       3050   49.31148   2500.346   50.00346          0 
         num |      3050       3050   2.698689   2.735354   1.653891          0 
    numeracy |      3050       3050   1.19e-08   2.735354   1.653891  -2.698689 
pct_incent~e |      3050       3050   66.68852   2222.222   47.14045          0 
nonstd_con~e |      3050       3050  -.1280328   2.747377   1.657521         -3 
conservative |      3050       3050  -8.94e-09          1          1  -1.732688 
   congenial |      3050       3050   .0025472   .9999935   .9999967  -1.887175 
         age |      3050       3050   52.38033   323.6874   17.99131         18 
  pct_female |      3036       3036   52.53623   2494.389   49.94386          0 
pct_race_nhw |      3050       3050   69.70492   2112.409   45.96095          0 
pct_race_h~c |      3050       3050   16.13115   1353.345   36.78783          0 
pct_race_o~r |      3050       3050   14.16393   1216.175    34.8737          0 
pct_edu_hi~l |      3050       3050   31.34426   2152.669   46.39687          0 
pct_edu_co~e |      3050       3050         52   2496.819   49.96818          0 
pct_edu_ot~r |      3050       3050   16.65574   1388.615   37.26413          0 
pct_vote20~p |      3050       3050    30.7541   2130.294   46.15511          0 
pct_vote20~n |      3050       3050   32.06557   2179.071   46.68052          0 
pct_vote20~e |      3050       3050   28.22951    2026.71     45.019          0 

             |    e(max)     e(sum) 
-------------+----------------------
 pct_correct |       100     128800 
pct_covid~nc |       100     154600 
pct_covid~ec |       100     150400 
         num |         6       8231 
    numeracy |  3.301311   .0000363 
pct_incent~e |       100     203400 
nonstd_con~e |         3     -390.5 
conservative |  1.887175  -.0000273 
   congenial |  1.887175   7.769058 
         age |        92     159760 
  pct_female |       100     159500 
pct_race_nhw |       100     212600 
pct_race_h~c |       100      49200 
pct_race_o~r |       100      43200 
pct_edu_hi~l |       100      95600 
pct_edu_co~e |       100     158600 
pct_edu_ot~r |       100      50800 
pct_vote20~p |       100      93800 
pct_vote20~n |       100      97800 
pct_vote20~e |       100      86100 

. 
. esttab using "${main_appendix}/Table_A7.tex", ///
>                                 cells((mean (fmt(2)) sd (fmt(2))))  label repla
> ce ///
>                                 nofloat
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A7.tex)

. eststo  clear 

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Balance table
. * Table A8
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * Table A8: Balance on observable covariates among treatment groups
. *------------------------------------------------------------------------------
> -
. * Generate new variables for balance table
. * Treatment
. * Treatment 1 = No incentive/Covid-decrease
. * Treatment 2 = No incentive/Covid-increase
. * Treatment 3 = Incentive/Covid-decrease
. * Treatment 4 = Incentive/Covid-increase
. gen treatment1 = 0 

. gen treatment2 = 0 

. gen treatment3 = 0 

. gen treatment4 = 0

. replace treatment1 = 1 if treatment == 1
(512 real changes made)

. replace treatment2 = 1 if treatment == 2
(504 real changes made)

. replace treatment3 = 1 if treatment == 3
(992 real changes made)

. replace treatment4 = 1 if treatment == 4
(1,042 real changes made)

. 
. * Calculate values in the Balance table
. foreach yvar in age female                                                     
>                          ///
>                                 race_nhw race_hispanic race_other              
>                  ///
>                                 edu_highschool edu_college edu_other           
>          ///
>                                 vote2016_trump vote2016_clinton vote2016_novote
> {
  2. 
. reg             `yvar' treatment2 treatment3 treatment4, robust
  3. reg             `yvar' treatment1 treatment3 treatment4, robust
  4. reg             `yvar' treatment1 treatment2 treatment4, robust
  5. predict         `yvar'_hat
  6. predict         `yvar'_se, stdp
  7. }

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.38
                                                Prob > F          =     0.7644
                                                R-squared         =     0.0004
                                                Root MSE          =     17.997

------------------------------------------------------------------------------
             |               Robust
         age | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.7247024   1.155777    -0.63   0.531    -2.990885     1.54148
  treatment3 |   .3064516   .9929463     0.31   0.758    -1.640461    2.253364
  treatment4 |   .1658469   .9856083     0.17   0.866    -1.766678    2.098372
       _cons |   52.34375   .8170859    64.06   0.000     50.74165    53.94585
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.38
                                                Prob > F          =     0.7644
                                                R-squared         =     0.0004
                                                Root MSE          =     17.997

------------------------------------------------------------------------------
             |               Robust
         age | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .7247024   1.155777     0.63   0.531     -1.54148    2.990885
  treatment3 |   1.031154   .9932296     1.04   0.299    -.9163141    2.978622
  treatment4 |   .8905493   .9858937     0.90   0.366    -1.042535    2.823634
       _cons |   51.61905   .8174301    63.15   0.000     50.01628    53.22182
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.38
                                                Prob > F          =     0.7644
                                                R-squared         =     0.0004
                                                Root MSE          =     17.997

------------------------------------------------------------------------------
             |               Robust
         age | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.3064516   .9929463    -0.31   0.758    -2.253364    1.640461
  treatment2 |  -1.031154   .9932296    -1.04   0.299    -2.978622    .9163141
  treatment4 |  -.1406047   .7887379    -0.18   0.859    -1.687117    1.405908
       _cons |    52.6502   .5641924    93.32   0.000     51.54397    53.75644
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,036
                                                F(3, 3032)        =       1.03
                                                Prob > F          =     0.3768
                                                R-squared         =     0.0010
                                                Root MSE          =     .49943

------------------------------------------------------------------------------
             |               Robust
      female | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |   .0202674   .0313351     0.65   0.518    -.0411728    .0817076
  treatment3 |  -.0263436   .0272594    -0.97   0.334    -.0797923    .0271051
  treatment4 |  -.0053895   .0270308    -0.20   0.842    -.0583901    .0476111
       _cons |   .5324165   .0221301    24.06   0.000      .489025     .575808
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,036
                                                F(3, 3032)        =       1.03
                                                Prob > F          =     0.3768
                                                R-squared         =     0.0010
                                                Root MSE          =     .49943

------------------------------------------------------------------------------
             |               Robust
      female | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0202674   .0313351    -0.65   0.518    -.0817076    .0411728
  treatment3 |   -.046611   .0273035    -1.71   0.088    -.1001463    .0069242
  treatment4 |  -.0256569   .0270753    -0.95   0.343    -.0787447     .027431
       _cons |   .5526839   .0221844    24.91   0.000     .5091859    .5961819
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,036
                                                F(3, 3032)        =       1.03
                                                Prob > F          =     0.3768
                                                R-squared         =     0.0010
                                                Root MSE          =     .49943

------------------------------------------------------------------------------
             |               Robust
      female | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0263436   .0272594     0.97   0.334    -.0271051    .0797923
  treatment2 |    .046611   .0273035     1.71   0.088    -.0069242    .1001463
  treatment4 |   .0209542   .0222319     0.94   0.346     -.022637    .0645453
       _cons |   .5060729   .0159164    31.80   0.000     .4748648     .537281
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.92
                                                Prob > F          =     0.1235
                                                R-squared         =     0.0019
                                                Root MSE          =     .45939

------------------------------------------------------------------------------
             |               Robust
    race_nhw | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |   .0145089   .0294892     0.49   0.623    -.0433118    .0723297
  treatment3 |   .0365423    .025456     1.44   0.151    -.0133704    .0864551
  treatment4 |   .0547475     .02511     2.18   0.029     .0055132    .1039817
       _cons |   .6640625   .0208874    31.79   0.000     .6231077    .7050173
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.92
                                                Prob > F          =     0.1235
                                                R-squared         =     0.0019
                                                Root MSE          =     .45939

------------------------------------------------------------------------------
             |               Robust
    race_nhw | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0145089   .0294892    -0.49   0.623    -.0723297    .0433118
  treatment3 |   .0220334    .025398     0.87   0.386    -.0277655    .0718323
  treatment4 |   .0402386   .0250512     1.61   0.108    -.0088803    .0893574
       _cons |   .6785714   .0208166    32.60   0.000     .6377554    .7193874
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.92
                                                Prob > F          =     0.1235
                                                R-squared         =     0.0019
                                                Root MSE          =     .45939

------------------------------------------------------------------------------
             |               Robust
    race_nhw | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0365423    .025456    -1.44   0.151    -.0864551    .0133704
  treatment2 |  -.0220334    .025398    -0.87   0.386    -.0718323    .0277655
  treatment4 |   .0182051   .0201484     0.90   0.366    -.0213006    .0577109
       _cons |   .7006048   .0145508    48.15   0.000     .6720744    .7291353
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.48
                                                Prob > F          =     0.2172
                                                R-squared         =     0.0015
                                                Root MSE          =     .36778

------------------------------------------------------------------------------
             |               Robust
race_hispa~c | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0010851   .0241797    -0.04   0.964    -.0484952     .046325
  treatment3 |  -.0263987   .0205689    -1.28   0.199    -.0667291    .0139317
  treatment4 |  -.0338479   .0202914    -1.67   0.095    -.0736341    .0059383
       _cons |   .1816406   .0170502    10.65   0.000     .1482096    .2150716
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.48
                                                Prob > F          =     0.2172
                                                R-squared         =     0.0015
                                                Root MSE          =     .36778

------------------------------------------------------------------------------
             |               Robust
race_hispa~c | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0010851   .0241797     0.04   0.964     -.046325    .0484952
  treatment3 |  -.0253136   .0206475    -1.23   0.220    -.0657981    .0151709
  treatment4 |  -.0327628    .020371    -1.61   0.108    -.0727052    .0071795
       _cons |   .1805556   .0171449    10.53   0.000     .1469388    .2141723
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.48
                                                Prob > F          =     0.2172
                                                R-squared         =     0.0015
                                                Root MSE          =     .36778

------------------------------------------------------------------------------
             |               Robust
race_hispa~c | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0263987   .0205689     1.28   0.199    -.0139317    .0667291
  treatment2 |   .0253136   .0206475     1.23   0.220    -.0151709    .0657981
  treatment4 |  -.0074492   .0159187    -0.47   0.640    -.0386617    .0237633
       _cons |   .1552419   .0115053    13.49   0.000     .1326829     .177801
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.43
                                                Prob > F          =     0.7315
                                                R-squared         =     0.0004
                                                Root MSE          =     .34883

------------------------------------------------------------------------------
             |               Robust
  race_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0134239   .0222631    -0.60   0.547    -.0570761    .0302284
  treatment3 |  -.0101436   .0194866    -0.52   0.603    -.0483519    .0280646
  treatment4 |  -.0208996   .0191386    -1.09   0.275    -.0584254    .0166263
       _cons |   .1542969   .0159749     9.66   0.000     .1229742    .1856195
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.43
                                                Prob > F          =     0.7315
                                                R-squared         =     0.0004
                                                Root MSE          =     .34883

------------------------------------------------------------------------------
             |               Robust
  race_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0134239   .0222631     0.60   0.547    -.0302284    .0570761
  treatment3 |   .0032802   .0191045     0.17   0.864    -.0341788    .0407392
  treatment4 |  -.0074757   .0187494    -0.40   0.690    -.0442384     .029287
       _cons |    .140873   .0155064     9.08   0.000     .1104689    .1712772
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.43
                                                Prob > F          =     0.7315
                                                R-squared         =     0.0004
                                                Root MSE          =     .34883

------------------------------------------------------------------------------
             |               Robust
  race_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0101436   .0194866     0.52   0.603    -.0280646    .0483519
  treatment2 |  -.0032802   .0191045    -0.17   0.864    -.0407392    .0341788
  treatment4 |  -.0107559   .0153499    -0.70   0.484    -.0408532    .0193413
       _cons |   .1441532   .0111594    12.92   0.000     .1222726    .1660339
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.26
                                                Prob > F          =     0.2859
                                                R-squared         =     0.0012
                                                Root MSE          =     .46391

------------------------------------------------------------------------------
             |               Robust
edu_highsc~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0125558   .0294678    -0.43   0.670    -.0703346     .045223
  treatment3 |  -.0124118   .0255975    -0.48   0.628     -.062602    .0377784
  treatment4 |  -.0422377   .0251711    -1.68   0.093    -.0915918    .0071163
       _cons |   .3339844   .0208572    16.01   0.000     .2930888    .3748799
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.26
                                                Prob > F          =     0.2859
                                                R-squared         =     0.0012
                                                Root MSE          =     .46391

------------------------------------------------------------------------------
             |               Robust
edu_highsc~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0125558   .0294678     0.43   0.670     -.045223    .0703346
  treatment3 |    .000144   .0255645     0.01   0.996    -.0499814    .0502694
  treatment4 |  -.0296819   .0251375    -1.18   0.238    -.0789701    .0196062
       _cons |   .3214286   .0208166    15.44   0.000     .2806126    .3622446
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.26
                                                Prob > F          =     0.2859
                                                R-squared         =     0.0012
                                                Root MSE          =     .46391

------------------------------------------------------------------------------
             |               Robust
edu_highsc~l | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0124118   .0255975     0.48   0.628    -.0377784     .062602
  treatment2 |   -.000144   .0255645    -0.01   0.996    -.0502694    .0499814
  treatment4 |  -.0298259    .020464    -1.46   0.145    -.0699505    .0102987
       _cons |   .3215726   .0148395    21.67   0.000     .2924761    .3506691
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.73
                                                Prob > F          =     0.5319
                                                R-squared         =     0.0007
                                                Root MSE          =     .49975

------------------------------------------------------------------------------
             |               Robust
 edu_college | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |    .031684   .0313695     1.01   0.313    -.0298234    .0931915
  treatment3 |   .0180192    .027222     0.66   0.508    -.0353562    .0713946
  treatment4 |   .0374955   .0269823     1.39   0.165    -.0154099    .0904009
       _cons |   .4960938   .0221109    22.44   0.000     .4527399    .5394476
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.73
                                                Prob > F          =     0.5319
                                                R-squared         =     0.0007
                                                Root MSE          =     .49975

------------------------------------------------------------------------------
             |               Robust
 edu_college | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   -.031684   .0313695    -1.01   0.313    -.0931915    .0298234
  treatment3 |  -.0136649   .0273367    -0.50   0.617    -.0672652    .0399354
  treatment4 |   .0058115    .027098     0.21   0.830    -.0473208    .0589438
       _cons |   .5277778    .022252    23.72   0.000     .4841474    .5714082
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.73
                                                Prob > F          =     0.5319
                                                R-squared         =     0.0007
                                                Root MSE          =     .49975

------------------------------------------------------------------------------
             |               Robust
 edu_college | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0180192    .027222    -0.66   0.508    -.0713946    .0353562
  treatment2 |   .0136649   .0273367     0.50   0.617    -.0399354    .0672652
  treatment4 |   .0194763   .0221653     0.88   0.380    -.0239841    .0629368
       _cons |   .5141129   .0158791    32.38   0.000     .4829781    .5452478
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.51
                                                Prob > F          =     0.6763
                                                R-squared         =     0.0005
                                                Root MSE          =     .37273

------------------------------------------------------------------------------
             |               Robust
   edu_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0191282   .0230273    -0.83   0.406    -.0642789    .0260225
  treatment3 |  -.0056074   .0203581    -0.28   0.783    -.0455243    .0343096
  treatment4 |   .0047422   .0203562     0.23   0.816     -.035171    .0446555
       _cons |   .1699219   .0166086    10.23   0.000     .1373566    .2024872
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.51
                                                Prob > F          =     0.6763
                                                R-squared         =     0.0005
                                                Root MSE          =     .37273

------------------------------------------------------------------------------
             |               Robust
   edu_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0191282   .0230273     0.83   0.406    -.0260225    .0642789
  treatment3 |   .0135209   .0198246     0.68   0.495    -.0253501    .0523918
  treatment4 |   .0238705   .0198227     1.20   0.229    -.0149967    .0627376
       _cons |   .1507937   .0159503     9.45   0.000     .1195193     .182068
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.51
                                                Prob > F          =     0.6763
                                                R-squared         =     0.0005
                                                Root MSE          =     .37273

------------------------------------------------------------------------------
             |               Robust
   edu_other | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0056074   .0203581     0.28   0.783    -.0343096    .0455243
  treatment2 |  -.0135209   .0198246    -0.68   0.495    -.0523918    .0253501
  treatment4 |   .0103496   .0166473     0.62   0.534    -.0222915    .0429906
       _cons |   .1643145    .011773    13.96   0.000     .1412306    .1873984
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.20
                                                Prob > F          =     0.8963
                                                R-squared         =     0.0002
                                                Root MSE          =     .46173

------------------------------------------------------------------------------
             |               Robust
vote2016_t~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0109437   .0289072    -0.38   0.705    -.0676233    .0457359
  treatment3 |   .0049773   .0252334     0.20   0.844    -.0444989    .0544535
  treatment4 |  -.0082436   .0249281    -0.33   0.741    -.0571211    .0406339
       _cons |   .3105469   .0204628    15.18   0.000     .2704245    .3506693
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.20
                                                Prob > F          =     0.8963
                                                R-squared         =     0.0002
                                                Root MSE          =     .46173

------------------------------------------------------------------------------
             |               Robust
vote2016_t~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0109437   .0289072     0.38   0.705    -.0457359    .0676233
  treatment3 |    .015921   .0251971     0.63   0.528     -.033484    .0653261
  treatment4 |   .0027001   .0248913     0.11   0.914    -.0461054    .0515056
       _cons |   .2996032   .0204181    14.67   0.000     .2595686    .3396378
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.20
                                                Prob > F          =     0.8963
                                                R-squared         =     0.0002
                                                Root MSE          =     .46173

------------------------------------------------------------------------------
             |               Robust
vote2016_t~p | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0049773   .0252334    -0.20   0.844    -.0544535    .0444989
  treatment2 |   -.015921   .0251971    -0.63   0.528    -.0653261     .033484
  treatment4 |  -.0132209   .0205104    -0.64   0.519    -.0534366    .0269947
       _cons |   .3155242   .0147647    21.37   0.000     .2865744     .344474
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.34
                                                Prob > F          =     0.2609
                                                R-squared         =     0.0013
                                                Root MSE          =     .46674

------------------------------------------------------------------------------
             |               Robust
vote2016_c~n | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |   .0521453   .0290301     1.80   0.073    -.0047752    .1090658
  treatment3 |   .0414567   .0249129     1.66   0.096    -.0073912    .0903045
  treatment4 |   .0392199    .024683     1.59   0.112    -.0091771     .087617
       _cons |   .2851562   .0199663    14.28   0.000     .2460075     .324305
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.34
                                                Prob > F          =     0.2609
                                                R-squared         =     0.0013
                                                Root MSE          =     .46674

------------------------------------------------------------------------------
             |               Robust
vote2016_c~n | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0521453   .0290301    -1.80   0.073    -.1090658    .0047752
  treatment3 |  -.0106887   .0258088    -0.41   0.679    -.0612931    .0399158
  treatment4 |  -.0129254   .0255869    -0.51   0.613    -.0630948     .037244
       _cons |   .3373016   .0210735    16.01   0.000     .2959818    .3786213
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       1.34
                                                Prob > F          =     0.2609
                                                R-squared         =     0.0013
                                                Root MSE          =     .46674

------------------------------------------------------------------------------
             |               Robust
vote2016_c~n | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |  -.0414567   .0249129    -1.66   0.096    -.0903045    .0073912
  treatment2 |   .0106887   .0258088     0.41   0.679    -.0399158    .0612931
  treatment4 |  -.0022367   .0207991    -0.11   0.914    -.0430183    .0385449
       _cons |   .3266129   .0148997    21.92   0.000     .2973984    .3558274
------------------------------------------------------------------------------
(option xb assumed; fitted values)

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.99
                                                Prob > F          =     0.3970
                                                R-squared         =     0.0010
                                                Root MSE          =     .45018

------------------------------------------------------------------------------
             |               Robust
vote2016_n~e | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment2 |  -.0347222   .0286136    -1.21   0.225    -.0908262    .0213818
  treatment3 |  -.0423387   .0248836    -1.70   0.089     -.091129    .0064516
  treatment4 |    -.03131    .024787    -1.26   0.207     -.079911    .0172911
       _cons |      .3125    .020498    15.25   0.000     .2723087    .3526913
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.99
                                                Prob > F          =     0.3970
                                                R-squared         =     0.0010
                                                Root MSE          =     .45018

------------------------------------------------------------------------------
             |               Robust
vote2016_n~e | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0347222   .0286136     1.21   0.225    -.0213818    .0908262
  treatment3 |  -.0076165   .0244458    -0.31   0.755    -.0555485    .0403155
  treatment4 |   .0034122   .0243475     0.14   0.889     -.044327    .0511515
       _cons |   .2777778   .0199643    13.91   0.000     .2386329    .3169226
------------------------------------------------------------------------------

Linear regression                               Number of obs     =      3,050
                                                F(3, 3046)        =       0.99
                                                Prob > F          =     0.3970
                                                R-squared         =     0.0010
                                                Root MSE          =     .45018

------------------------------------------------------------------------------
             |               Robust
vote2016_n~e | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  treatment1 |   .0423387   .0248836     1.70   0.089    -.0064516     .091129
  treatment2 |   .0076165   .0244458     0.31   0.755    -.0403155    .0555485
  treatment4 |   .0110287   .0198307     0.56   0.578    -.0278541    .0499116
       _cons |   .2701613   .0141076    19.15   0.000     .2424998    .2978227
------------------------------------------------------------------------------
(option xb assumed; fitted values)

. *******************************************************************************
> ****************************************************************
.                         *******The collapsed data is manually formatted to crea
> te Table A8********************
. *******************************************************************************
> ****************************************************************
. 
. collapse        (mean)  mean_age = age                                         
>                  (semean) se_age = age                                         
>                   ///
>                         (mean)  mean_female = female                           
>                  (semean) se_female = female                                   
>                   ///
>                         (mean)  mean_race_nhw = race_nhw                       
>                  (semean) se_race_nhw = race_nhw                               
>           ///
>                         (mean)  mean_race_hispanic  = race_hispanic            
>  (semean) se_race_hispanic = race_hispanic                       ///
>                         (mean)  mean_race_other = race_other                   
>          (semean) se_race_other = race_other                                   
>   ///
>                         (mean)  mean_edu_highschool = edu_highschool           
>  (semean) se_edu_highschool = edu_highschool                     ///
>                         (mean)  mean_edu_college = edu_college                 
>          (semean) se_edu_college = edu_college                           ///
>                         (mean)  mean_edu_other = edu_other                     
>          (semean) se_edu_other = edu_other                                     
>   ///
>                         (mean)  mean_vote2016_trump = vote2016_trump           
>  (semean) se_vote2016_trump = vote2016_trump                     ///
>                         (mean)  mean_vote2016_clinton = vote2016_clinton       
>  (semean) se_vote2016_clinton = vote2016_clinton         ///
>                         (mean)  mean_vote2016_novote = vote2016_novote         
>  (semean) se_vote2016_novote = vote2016_novote           ///
>                         ,by (treatment)

. 
. list

     +-------------------------------------------------------------------------+
  1. |      treatment |  mean_age |    se_age | mean_f~e | se_fem~e | mean_r~w |
     | noin_covid_dec |  52.34375 | .81734848 | .5324165 | .0221372 | .6640625 |
     |-------------------------------------------------------------------------|
     | se_rac~w  | mean_r~c  | se_rac~c  | mean_r~r  |  se_rac~r  |  mean_e~l  |
     | .0208941  | .1816406  | .0170556  | .1542969  |    .01598  |  .3339844  |
     |-----------+-----------+-----------+-----------+------------+------------|
     | se_edu~l  | mean_e~e  | se_edu~e  | mean_e~r  |  se_edu~r  |  mean_v~p  |
     | .0208639  | .4960938  |  .022118  | .1699219  |   .016614  |  .3105469  |
     |-------------------------------------------------------------------------|
     |  se_vot~p   |   mean_v~n   |   se_vot~n   |   mean_v~e   |   se_vot~e   |
     |  .0204694   |   .2851563   |   .0199727   |      .3125   |   .0205046   |
     +-------------------------------------------------------------------------+

     +-------------------------------------------------------------------------+
  2. |      treatment |  mean_age |    se_age | mean_f~e | se_fem~e | mean_r~w |
     | noin_covid_inc | 51.619049 | .81770551 | .5526839 | .0221919 | .6785714 |
     |-------------------------------------------------------------------------|
     | se_rac~w  | mean_r~c  | se_rac~c  | mean_r~r  |  se_rac~r  |  mean_e~l  |
     | .0208236  | .1805556  | .0171507  |  .140873  |  .0155117  |  .3214286  |
     |-----------+-----------+-----------+-----------+------------+------------|
     | se_edu~l  | mean_e~e  | se_edu~e  | mean_e~r  |  se_edu~r  |  mean_v~p  |
     | .0208236  | .5277778  | .0222595  | .1507937  |  .0159556  |  .2996032  |
     |-------------------------------------------------------------------------|
     |  se_vot~p   |   mean_v~n   |   se_vot~n   |   mean_v~e   |   se_vot~e   |
     |   .020425   |   .3373016   |   .0210806   |   .2777778   |    .019971   |
     +-------------------------------------------------------------------------+

     +-------------------------------------------------------------------------+
  3. |      treatment |  mean_age |    se_age | mean_f~e | se_fem~e | mean_r~w |
     |   in_covid_dec |   52.6502 |  .5641067 | .5060729 |  .015914 | .7006049 |
     |-------------------------------------------------------------------------|
     | se_rac~w  | mean_r~c  | se_rac~c  | mean_r~r  |  se_rac~r  |  mean_e~l  |
     | .0145486  | .1552419  | .0115036  | .1441532  |  .0111577  |  .3215726  |
     |-----------+-----------+-----------+-----------+------------+------------|
     | se_edu~l  | mean_e~e  | se_edu~e  | mean_e~r  |  se_edu~r  |  mean_v~p  |
     | .0148373  | .5141129  | .0158767  | .1643145  |  .0117712  |  .3155242  |
     |-------------------------------------------------------------------------|
     |  se_vot~p   |   mean_v~n   |   se_vot~n   |   mean_v~e   |   se_vot~e   |
     |  .0147625   |   .3266129   |   .0148975   |   .2701613   |   .0141055   |
     +-------------------------------------------------------------------------+

     +-------------------------------------------------------------------------+
  4. |      treatment |  mean_age |    se_age | mean_f~e | se_fem~e | mean_r~w |
     |   in_covid_inc | 52.509598 | .55107838 |  .527027 |  .015519 |   .71881 |
     |-------------------------------------------------------------------------|
     | se_rac~w  | mean_r~c  | se_rac~c  | mean_r~r  |  se_rac~r  |  mean_e~l  |
     | .0139342  | .1477927  | .0109995  | .1333973  |   .010538  |  .2917466  |
     |-----------+-----------+-----------+-----------+------------+------------|
     | se_edu~l  | mean_e~e  | se_edu~e  | mean_e~r  |  se_edu~r  |  mean_v~p  |
     | .0140887  | .5335892  | .0154619  | .1746641  |  .0117677  |  .3023033  |
     |-------------------------------------------------------------------------|
     |  se_vot~p   |   mean_v~n   |   se_vot~n   |   mean_v~e   |   se_vot~e   |
     |  .0142341   |   .3243762   |   .0145095   |     .28119   |   .0139342   |
     +-------------------------------------------------------------------------+

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Reload data
. use "${main_data}/pol_v0.8.dta", clear
(Merges randomization data with pol_v0.5)

. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * Difference-in-means
. * Table A9-A12
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. 
. /*Table A9: Differences in accuracy by levels of congeniality 
> (unincentivized participants) */
. 
. su congenial, detail

           measure of attitude-consistent message
-------------------------------------------------------------
      Percentiles      Smallest
 1%    -1.887175      -1.887175
 5%    -1.732688      -1.887175
10%    -1.431033      -1.887175       Obs               3,050
25%     -.680554      -1.887175       Sum of wgt.       3,050

50%    -.0772435                      Mean           .0025472
                        Largest       Std. dev.      .9999967
75%      .680554       1.887175
90%     1.431033       1.887175       Variance       .9999935
95%     1.732688       1.887175       Skewness      -.0114069
99%     1.887175       1.887175       Kurtosis       2.275447

. 
. gen uncongenial25 = 0

. replace uncongenial25 = 1 if congenial<-.680554
(733 real changes made)

. tab uncongenial25

uncongenial |
         25 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,317       75.97       75.97
          1 |        733       24.03      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. gen congenial50 = 0

. replace congenial50 = 1 if congenial>-.0772435
(1,520 real changes made)

. tab congenial50

congenial50 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,530       50.16       50.16
          1 |      1,520       49.84      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. 
. gen congenial75 = 0

. replace congenial75 = 1 if congenial>.680554
(747 real changes made)

. tab congenial75

congenial75 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,303       75.51       75.51
          1 |        747       24.49      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. mat T = J(1,5,.)

. 
. ttest correct if incentive==0, by(uncongenial25)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     775    .4477419    .0178737    .4975827    .4126553    .4828286
       1 |     241    .3443983    .0306722    .4761606    .2839772    .4048194
---------+--------------------------------------------------------------------
Combined |   1,016    .4232283     .015508    .4943143    .3927969    .4536598
---------+--------------------------------------------------------------------
    diff |            .1033436    .0363311                .0320508    .1746364
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   2.8445
H0: diff = 0                                     Degrees of freedom =     1014

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9977         Pr(|T| > |t|) = 0.0045          Pr(T > t) = 0.0023

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. 
. mat rownames T =  "Accuracy rate"  

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality more than 25th pct=0, Congeniality less than 2
> 5th pct=1, Difference, t-statistic, p-value)

              ----------------------------------------------------
                               Congeniality more than 25th pct=0 
              ----------------------------------------------------
               Accuracy rate                 0.45                
              ----------------------------------------------------


  -----------------------------------------------------------------------------
                   Congeniality less than 25th pct=1  Difference  t-statistic 
  -----------------------------------------------------------------------------
   Accuracy rate                 0.34                    0.10        2.84     
  -----------------------------------------------------------------------------


                           --------------------------
                                            p-value 
                           --------------------------
                            Accuracy rate    0.00   
                           --------------------------


. 
. ttest correct if incentive==0, by(congenial50)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     512     .390625     .021583    .4883676    .3482227    .4330273
       1 |     504    .4563492    .0222088    .4985858    .4127158    .4999826
---------+--------------------------------------------------------------------
Combined |   1,016    .4232283     .015508    .4943143    .3927969    .4536598
---------+--------------------------------------------------------------------
    diff |           -.0657242    .0309636               -.1264842   -.0049642
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.1226
H0: diff = 0                                     Degrees of freedom =     1014

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0170         Pr(|T| > |t|) = 0.0340          Pr(T > t) = 0.9830

. 
. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. mat rownames T =  "Accuracy rate"  

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 50th pct=0, Congeniality more than 5
> 0th pct=1, Difference, t-statistic, p-value)

              ----------------------------------------------------
                               Congeniality less than 50th pct=0 
              ----------------------------------------------------
               Accuracy rate                 0.39                
              ----------------------------------------------------


  -----------------------------------------------------------------------------
                   Congeniality more than 50th pct=1  Difference  t-statistic 
  -----------------------------------------------------------------------------
   Accuracy rate                 0.46                   -0.07        -2.12    
  -----------------------------------------------------------------------------


                           --------------------------
                                            p-value 
                           --------------------------
                            Accuracy rate    0.03   
                           --------------------------


. 
. ttest correct if incentive==0, by(congenial75)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     758    .4076517    .0178602    .4917223    .3725904     .442713
       1 |     258    .4689922    .0311291    .5000075    .4076916    .5302929
---------+--------------------------------------------------------------------
Combined |   1,016    .4232283     .015508    .4943143    .3927969    .4536598
---------+--------------------------------------------------------------------
    diff |           -.0613405    .0355946               -.1311881     .008507
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.7233
H0: diff = 0                                     Degrees of freedom =     1014

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0426         Pr(|T| > |t|) = 0.0851          Pr(T > t) = 0.9574

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. mat rownames T =  "Accuracy rate"  

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

              ----------------------------------------------------
                               Congeniality less than 75th pct=0 
              ----------------------------------------------------
               Accuracy rate                 0.41                
              ----------------------------------------------------


  -----------------------------------------------------------------------------
                   Congeniality more than 75th pct=1  Difference  t-statistic 
  -----------------------------------------------------------------------------
   Accuracy rate                 0.47                   -0.06        -1.72    
  -----------------------------------------------------------------------------


                           --------------------------
                                            p-value 
                           --------------------------
                            Accuracy rate    0.09   
                           --------------------------


. 
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. 
. /*Table A10: Differences in accuracy by levels of congeniality and numeracy 
> (unincentivized participants)
> */
.         
. su numeracy, detail

          numeracy standardized to be centered at 0
-------------------------------------------------------------
      Percentiles      Smallest
 1%    -2.698689      -2.698689
 5%    -2.698689      -2.698689
10%    -1.698689      -2.698689       Obs               3,050
25%    -1.698689      -2.698689       Sum of wgt.       3,050

50%    -.6986885                      Mean           1.19e-08
                        Largest       Std. dev.      1.653891
75%     1.301311       3.301311
90%     2.301311       3.301311       Variance       2.735354
95%     3.301311       3.301311       Skewness       .3102913
99%     3.301311       3.301311       Kurtosis       2.236921

. ** 0.5 SD = 1.653891/2=0.8269455
. gen less_num = 0

. replace less_num = 1 if numeracy< -0.8269455
(817 real changes made)

. tab less_num

   less_num |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,233       73.21       73.21
          1 |        817       26.79      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. gen more_num = 0

. replace more_num = 1 if numeracy> 0.8269455
(947 real changes made)

. tab more_num

   more_num |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,103       68.95       68.95
          1 |        947       31.05      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. *** Strongly uncongenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & less_num==1, by(uncongenial25)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     218    .4587156    .0338263    .4994395    .3920454    .5253858
       1 |      56    .3571429    .0646096    .4834938    .2276624    .4866233
---------+--------------------------------------------------------------------
Combined |     274    .4379562    .0300275    .4970435    .3788413    .4970711
---------+--------------------------------------------------------------------
    diff |            .1015727    .0743463               -.0447946      .24794
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   1.3662
H0: diff = 0                                     Degrees of freedom =      272

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9135         Pr(|T| > |t|) = 0.1730          Pr(T > t) = 0.0865

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==0 & more_num==1, by(uncongenial25)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     234    .4316239    .0324484    .4963644    .3676943    .4955536
       1 |      83    .3373494    .0522126    .4756794    .2334819    .4412169
---------+--------------------------------------------------------------------
Combined |     317    .4069401    .0276357    .4920402    .3525668    .4613134
---------+--------------------------------------------------------------------
    diff |            .0942745    .0627365                -.029161    .2177101
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   1.5027
H0: diff = 0                                     Degrees of freedom =      315

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9330         Pr(|T| > |t|) = 0.1339          Pr(T > t) = 0.0670

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality MORE than 25th pct=0, Congeniality LESS than 2
> 5th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality MORE than 25th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.46                
      Accuracy rate for more numerate                 0.43                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality LESS than 25th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.36                
      Accuracy rate for more numerate                 0.34                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate      0.10        1.37       0.17   
       Accuracy rate for more numerate      0.09        1.50       0.13   
      ---------------------------------------------------------------------


. 
.         
. *** Rather congenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & less_num==1, by(congenial50)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     126    .4444444    .0444444    .4988877    .3564834    .5324055
       1 |     148    .4324324     .040861    .4970958    .3516815    .5131833
---------+--------------------------------------------------------------------
Combined |     274    .4379562    .0300275    .4970435    .3788413    .4970711
---------+--------------------------------------------------------------------
    diff |             .012012    .0603558               -.1068118    .1308359
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.1990
H0: diff = 0                                     Degrees of freedom =      272

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5788         Pr(|T| > |t|) = 0.8424          Pr(T > t) = 0.4212

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==0 & more_num==1, by(congenial50)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     170    .3470588    .0366181     .477441    .2747711    .4193465
       1 |     147    .4761905    .0413334    .5011403    .3945015    .5578795
---------+--------------------------------------------------------------------
Combined |     317    .4069401    .0276357    .4920402    .3525668    .4613134
---------+--------------------------------------------------------------------
    diff |           -.1291317    .0550265               -.2373976   -.0208657
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.3467
H0: diff = 0                                     Degrees of freedom =      315

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0098         Pr(|T| > |t|) = 0.0196          Pr(T > t) = 0.9902

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 50th pct=0, Congeniality more than 5
> 0th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality less than 50th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.44                
      Accuracy rate for more numerate                 0.35                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality more than 50th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.43                
      Accuracy rate for more numerate                 0.48                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate      0.01        0.20       0.84   
       Accuracy rate for more numerate     -0.13        -2.35      0.02   
      ---------------------------------------------------------------------


. 
. 
.         
. *** Strongly congenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & less_num==1, by(congenial75)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     207    .4396135    .0345817    .4975433    .3714342    .5077929
       1 |      67    .4328358    .0609879    .4992079    .3110695    .5546022
---------+--------------------------------------------------------------------
Combined |     274    .4379562    .0300275    .4970435    .3788413    .4970711
---------+--------------------------------------------------------------------
    diff |            .0067777    .0699901               -.1310134    .1445688
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.0968
H0: diff = 0                                     Degrees of freedom =      272

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5385         Pr(|T| > |t|) = 0.9229          Pr(T > t) = 0.4615

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==0 & more_num==1, by(congenial75)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     231    .3766234    .0319496    .4855914    .3136721    .4395746
       1 |      86    .4883721    .0542179    .5027966    .3805723    .5961719
---------+--------------------------------------------------------------------
Combined |     317    .4069401    .0276357    .4920402    .3525668    .4613134
---------+--------------------------------------------------------------------
    diff |           -.1117487    .0619342               -.2336057    .0101083
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.8043
H0: diff = 0                                     Degrees of freedom =      315

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0361         Pr(|T| > |t|) = 0.0721          Pr(T > t) = 0.9639

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality less than 75th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.44                
      Accuracy rate for more numerate                 0.38                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality more than 75th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.43                
      Accuracy rate for more numerate                 0.49                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate      0.01        0.10       0.92   
       Accuracy rate for more numerate     -0.11        -1.80      0.07   
      ---------------------------------------------------------------------


.         
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
.         
. /*Table A11: Differences in accuracy by incentive*/     
. 
. mat T = J(1,5,.)

. 
. ttest correct,by(incentive)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |   1,016    .4232283     .015508    .4943143    .3927969    .4536598
       1 |   2,034    .4218289    .0109529    .4939729    .4003489    .4433089
---------+--------------------------------------------------------------------
Combined |   3,050    .4222951     .008945     .494006    .4047562     .439834
---------+--------------------------------------------------------------------
    diff |            .0013994    .0189815               -.0358184    .0386173
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.0737
H0: diff = 0                                     Degrees of freedom =     3048

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5294         Pr(|T| > |t|) = 0.9412          Pr(T > t) = 0.4706

. 
. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. 
. mat rownames T =  "Accuracy rate"  

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Incentive=0, Incentive=1, Difference, t-statistic, p-value)

  -----------------------------------------------------------------------------
                   Incentive=0  Incentive=1  Difference  t-statistic  p-value 
  -----------------------------------------------------------------------------
   Accuracy rate      0.42         0.42         0.00        0.07       0.94   
  -----------------------------------------------------------------------------


. 
.         
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. 
. /*Table A12: Differences in accuracy by levels of congeniality and numeracy 
> (incentivized participants)*/   
. 
. 
. *** Strongly uncongenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==1 & less_num==1, by(uncongenial25)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     418    .3875598     .023858     .487777     .340663    .4344567
       1 |     125        .416    .0442631     .494877    .3283908    .5036092
---------+--------------------------------------------------------------------
Combined |     543    .3941068    .0209897    .4891086    .3528758    .4353379
---------+--------------------------------------------------------------------
    diff |           -.0284402    .0498922               -.1264464     .069566
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -0.5700
H0: diff = 0                                     Degrees of freedom =      541

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.2844         Pr(|T| > |t|) = 0.5689          Pr(T > t) = 0.7156

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & more_num==1, by(uncongenial25)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     468    .5106838     .023132    .5004208    .4652281    .5561394
       1 |     162     .382716    .0383061     .487557    .3070689    .4583632
---------+--------------------------------------------------------------------
Combined |     630    .4777778    .0199166    .4999028    .4386667    .5168889
---------+--------------------------------------------------------------------
    diff |            .1279677    .0453191                .0389724     .216963
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   2.8237
H0: diff = 0                                     Degrees of freedom =      628

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9976         Pr(|T| > |t|) = 0.0049          Pr(T > t) = 0.0024

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality MORE than 25th pct=0, Congeniality LESS than 2
> 5th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality MORE than 25th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.39                
      Accuracy rate for more numerate                 0.51                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality LESS than 25th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.42                
      Accuracy rate for more numerate                 0.38                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate     -0.03        -0.57      0.57   
       Accuracy rate for more numerate      0.13        2.82       0.00   
      ---------------------------------------------------------------------


. 
.         
. *** Rather congenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==1 & less_num==1, by(congenial50)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     272    .4007353    .0297683    .4909508    .3421288    .4593418
       1 |     271    .3874539    .0296481    .4880701    .3290829    .4458248
---------+--------------------------------------------------------------------
Combined |     543    .3941068    .0209897    .4891086    .3528758    .4353379
---------+--------------------------------------------------------------------
    diff |            .0132814    .0420143               -.0692497    .0958125
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.3161
H0: diff = 0                                     Degrees of freedom =      541

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.6240         Pr(|T| > |t|) = 0.7520          Pr(T > t) = 0.3760

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & more_num==1, by(congenial50)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     309    .4401294    .0282852    .4972078    .3844728     .495786
       1 |     321    .5140187    .0279399    .5005838    .4590497    .5689877
---------+--------------------------------------------------------------------
Combined |     630    .4777778    .0199166    .4999028    .4386667    .5168889
---------+--------------------------------------------------------------------
    diff |           -.0738892     .039763               -.1519737    .0041953
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.8582
H0: diff = 0                                     Degrees of freedom =      628

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0318         Pr(|T| > |t|) = 0.0636          Pr(T > t) = 0.9682

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 50th pct=0, Congeniality more than 5
> 0th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality less than 50th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.40                
      Accuracy rate for more numerate                 0.44                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality more than 50th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.39                
      Accuracy rate for more numerate                 0.51                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate      0.01        0.32       0.75   
       Accuracy rate for more numerate     -0.07        -1.86      0.06   
      ---------------------------------------------------------------------


. 
. 
.         
. *** Strongly congenial data ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==1 & less_num==1, by(congenial75)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     411    .3819951    .0239957    .4864675    .3348252     .429165
       1 |     132    .4318182    .0432771    .4972164    .3462057    .5174307
---------+--------------------------------------------------------------------
Combined |     543    .3941068    .0209897    .4891086    .3528758    .4353379
---------+--------------------------------------------------------------------
    diff |            -.049823    .0489308               -.1459407    .0462946
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.0182
H0: diff = 0                                     Degrees of freedom =      541

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.1545         Pr(|T| > |t|) = 0.3090          Pr(T > t) = 0.8455

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & more_num==1, by(congenial75)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |     463    .4319654    .0230458    .4958855     .386678    .4772529
       1 |     167    .6047904    .0379457     .490366    .5298721    .6797087
---------+--------------------------------------------------------------------
Combined |     630    .4777778    .0199166    .4999028    .4386667    .5168889
---------+--------------------------------------------------------------------
    diff |            -.172825    .0446302               -.2604674   -.0851825
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.8724
H0: diff = 0                                     Degrees of freedom =      628

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0001         Pr(|T| > |t|) = 0.0001          Pr(T > t) = 0.9999

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Accuracy rate for less numerate"  "Accuracy rate for more nu
> merate"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

     ----------------------------------------------------------------------
                                        Congeniality less than 75th pct=0 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.38                
      Accuracy rate for more numerate                 0.43                
     ----------------------------------------------------------------------


     ----------------------------------------------------------------------
                                        Congeniality more than 75th pct=1 
     ----------------------------------------------------------------------
      Accuracy rate for less numerate                 0.43                
      Accuracy rate for more numerate                 0.60                
     ----------------------------------------------------------------------


      ---------------------------------------------------------------------
                                         Difference  t-statistic  p-value 
      ---------------------------------------------------------------------
       Accuracy rate for less numerate     -0.05        -1.02      0.31   
       Accuracy rate for more numerate     -0.17        -3.87      0.00   
      ---------------------------------------------------------------------


.         
. drop uncongenial25 congenial50 congenial75 more_num less_num 

. 
. *------------------------------------------------------------------------------
> -
. 
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Inferiority tests
. * Logistic regression - Logit model is used in these two tables
. * Table A13&A14: The impact of incentives, numeracy and congeniality on accurac
> y
. * Table A13 for unincentivized paticipants
. * Table A14 for all participants
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * Table A13: The impact of numeracy and congeniality on accuracy (unincentivize
> d)
. *------------------------------------------------------------------------------
> -
. * Adjust the label values to accomodate the table
. label var correct "Correct"

. label var incentive "Incentive"

. label var congenial "Congenial"

. label var numeracy "Numeracy"

. label var numsq "Numeracy$^2$"

. label var num_con "Numeracy $\times$ Congenial"

. label var in_num_con "Incentive $\times$ Numeracy $\times$ Congenial"

. label var in_con "Incentive $\times$ Congenial"

. label var in_num "Incentive $\times$ Numeracy"

. label var in_numsq "Incentive $\times$ Numeracy$^2$"

. label var in_numsq_con "Incentive $\times$ Numeracy$^2$ $\times$ Congenial"

. 
. * Equation 1 (without control variables) - Table A13 (1)
. logit correct congenial numeracy numsq if incentive==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -687.26035  
Iteration 2:   log pseudolikelihood = -687.25892  
Iteration 3:   log pseudolikelihood = -687.25892  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(3)  =   9.81
                                                        Prob > chi2   = 0.0203
Log pseudolikelihood = -687.25892                       Pseudo R2     = 0.0072

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .1968687   .0647235     3.04   0.002     .0700129    .3237245
    numeracy |  -.0170448   .0395878    -0.43   0.667    -.0946355    .0605459
       numsq |     .01329   .0219693     0.60   0.545     -.029769     .056349
       _cons |   -.350974   .0880149    -3.99   0.000      -.52348    -.178468
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A13 (2)
. logit correct  congenial numeracy numsq age i.gender i.race i.edu i.vote2016 if
>  incentive==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -673.11806  
Iteration 2:   log pseudolikelihood = -673.05536  
Iteration 3:   log pseudolikelihood = -673.05519  
Iteration 4:   log pseudolikelihood = -673.05519  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(23) =  37.13
                                                        Prob > chi2   = 0.0315
Log pseudolikelihood = -673.05519                       Pseudo R2     = 0.0277

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .1863094   .0662187     2.81   0.005     .0565231    .3160958
      numeracy |   -.022684   .0434842    -0.52   0.602    -.1079114    .0625434
         numsq |   .0195446   .0226466     0.86   0.388     -.024842    .0639312
           age |   .0054923   .0043433     1.26   0.206    -.0030204     .014005
               |
        gender |
         Male  |      .1253   .1397346     0.90   0.370    -.1485747    .3991748
        Other  |   .4035975   1.270023     0.32   0.751    -2.085601    2.892796
      Not say  |  -.3336888   1.447534    -0.23   0.818    -3.170804    2.503427
               |
          race |
Non-hispani..  |   .3918077   .3149994     1.24   0.214    -.2255798    1.009195
     Hispanic  |   .5740312   .1902672     3.02   0.003     .2011143    .9469481
        Asian  |   .6148646   .3261964     1.88   0.059    -.0244685    1.254198
American In..  |  -.9783342   1.102514    -0.89   0.375    -3.139222    1.182554
       Others  |    .354886   .4054531     0.88   0.381    -.4397876     1.14956
Prefer not ..  |   .7884453   .6288703     1.25   0.210    -.4441178    2.021008
               |
           edu |
High school..  |  -.2171242    .322009    -0.67   0.500    -.8482503    .4140019
 Some college  |  -.5271984   .3326746    -1.58   0.113    -1.179229    .1248318
 College grad  |  -.5194518   .3386973    -1.53   0.125    -1.183286    .1443827
    Post grad  |  -.1728757   .3577042    -0.48   0.629    -.8739631    .5282118
        Other  |  -1.148193   .8879274    -1.29   0.196    -2.888499    .5921127
               |
      vote2016 |
      Clinton  |  -.1736134   .1684016    -1.03   0.303    -.5036745    .1564476
Other candi..  |   .2929844   .3145814     0.93   0.352    -.3235838    .9095527
      No vote  |  -.2528106   .1947511    -1.30   0.194    -.6345158    .1288945
      Not say  |   .2900093    .379987     0.76   0.445    -.4547516     1.03477
        Other  |  -.0125566   .7117286    -0.02   0.986    -1.407519    1.382406
               |
         _cons |   -.418357   .4225998    -0.99   0.322    -1.246637    .4099233
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Equation 2 (without control variables) - Table A13 (3)
. logit correct congenial numeracy numsq num_con c.numsq#c.congenial  if incentiv
> e==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -685.66062  
Iteration 2:   log pseudolikelihood = -685.65559  
Iteration 3:   log pseudolikelihood = -685.65559  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(5)  =  12.63
                                                        Prob > chi2   = 0.0272
Log pseudolikelihood = -685.65559                       Pseudo R2     = 0.0095

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .2338905   .0911453     2.57   0.010      .055249     .412532
    numeracy |  -.0213004    .039582    -0.54   0.590    -.0988797    .0562789
       numsq |   .0146061   .0220094     0.66   0.507    -.0285316    .0577438
     num_con |   .0725903   .0407434     1.78   0.075    -.0072654    .1524459
             |
     c.numsq#|
 c.congenial |  -.0145652   .0231521    -0.63   0.529    -.0599424     .030812
             |
       _cons |   -.353564   .0883086    -4.00   0.000    -.5266457   -.1804823
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table A13 (4)
. logit correct congenial numeracy numsq num_con c.numsq#c.congenial age i.gender
>  i.race i.edu i.vote2016 if incentive==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -671.99629  
Iteration 2:   log pseudolikelihood = -671.92327  
Iteration 3:   log pseudolikelihood = -671.92309  
Iteration 4:   log pseudolikelihood = -671.92309  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(25) =  38.70
                                                        Prob > chi2   = 0.0395
Log pseudolikelihood = -671.92309                       Pseudo R2     = 0.0293

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .2187995   .0928563     2.36   0.018     .0368044    .4007945
      numeracy |  -.0266865    .043422    -0.61   0.539    -.1117921    .0584191
         numsq |   .0206906   .0226845     0.91   0.362    -.0237702    .0651513
       num_con |   .0622858   .0416394     1.50   0.135    -.0193258    .1438975
               |
       c.numsq#|
   c.congenial |  -.0125362   .0237474    -0.53   0.598    -.0590803    .0340079
               |
           age |   .0055738   .0043411     1.28   0.199    -.0029346    .0140822
               |
        gender |
         Male  |   .1232536   .1399168     0.88   0.378    -.1509783    .3974855
        Other  |   .3541774   1.253841     0.28   0.778    -2.103306    2.811661
      Not say  |  -.3755975   1.426736    -0.26   0.792    -3.171948    2.420753
               |
          race |
Non-hispani..  |   .3598705   .3134651     1.15   0.251    -.2545098    .9742508
     Hispanic  |    .564039   .1901613     2.97   0.003     .1913297    .9367482
        Asian  |   .5930115   .3287583     1.80   0.071     -.051343    1.237366
American In..  |   -1.04169   1.118879    -0.93   0.352    -3.234652    1.151273
       Others  |   .3419818   .4062594     0.84   0.400     -.454272    1.138236
Prefer not ..  |   .8058624   .6239868     1.29   0.197    -.4171293    2.028854
               |
           edu |
High school..  |  -.2219449   .3190735    -0.70   0.487    -.8473174    .4034276
 Some college  |  -.5242756   .3299547    -1.59   0.112    -1.170975    .1224238
 College grad  |   -.511631   .3355434    -1.52   0.127    -1.169284     .146022
    Post grad  |   -.177815   .3551517    -0.50   0.617    -.8738997    .5182696
        Other  |  -1.167153   .9085463    -1.28   0.199    -2.947871     .613565
               |
      vote2016 |
      Clinton  |  -.1827024   .1693434    -1.08   0.281    -.5146093    .1492045
Other candi..  |   .2707574   .3152614     0.86   0.390    -.3471435    .8886583
      No vote  |  -.2505398   .1941988    -1.29   0.197    -.6311626    .1300829
      Not say  |   .2835271   .3814338     0.74   0.457    -.4640695    1.031124
        Other  |   .0009651   .7190858     0.00   0.999    -1.408417    1.410347
               |
         _cons |  -.4157697   .4212075    -0.99   0.324    -1.241321    .4097819
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Export Table A13 in Latex
. esttab  a1 a2 a3 a4 using "${main_appendix}/Table_A13.tex",  ///
>                 eqlabel(none) nonumbers mtitles("(1)" "(2)" "(3)" "(4)") b(3) s
> tar(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Logit regression with heterscedasticity robu
> st standard errors." "Control variables in the regression are age, gender, race
> , education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A13.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A14: The impact of incentives, numeracy, and congeniality on accuracy (
> all)
. *------------------------------------------------------------------------------
> -
. * Equation 3 (without control variables) - Table A14 (5)
. logit correct incentive, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2077.1143  
Iteration 2:   log pseudolikelihood = -2077.1143  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(1)  =   0.01
                                                        Prob > chi2   = 0.9412
Log pseudolikelihood = -2077.1143                       Pseudo R2     = 0.0000

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |  -.0057354    .077781    -0.07   0.941    -.1581835    .1467126
       _cons |  -.3095346    .063509    -4.87   0.000    -.4340099   -.1850593
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A14 (6)
. logit correct incentive age i.gender i.race i.edu i.vote2016, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2063.0942  
Iteration 2:   log pseudolikelihood = -2063.0836  
Iteration 3:   log pseudolikelihood = -2063.0836  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(21) =  27.77
                                                        Prob > chi2   = 0.1468
Log pseudolikelihood = -2063.0836                       Pseudo R2     = 0.0068

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |  -.0070454   .0781388    -0.09   0.928    -.1601945    .1461037
           age |   .0014021   .0024559     0.57   0.568    -.0034113    .0062156
               |
        gender |
         Male  |   .1637638   .0765585     2.14   0.032     .0137119    .3138157
        Other  |  -.3060898   .8296312    -0.37   0.712    -1.932137    1.319958
      Not say  |   .9330308   .7723567     1.21   0.227    -.5807606    2.446822
               |
          race |
Non-hispani..  |   .1361987   .1718378     0.79   0.428    -.2005972    .4729946
     Hispanic  |    .226152     .11278     2.01   0.045     .0051073    .4471967
        Asian  |   .1713442   .1750056     0.98   0.328    -.1716603    .5143488
American In..  |  -.1336213   .5462036    -0.24   0.807    -1.204161     .936918
       Others  |   .0164908    .247544     0.07   0.947    -.4686865     .501668
Prefer not ..  |   .1876689    .355086     0.53   0.597    -.5082868    .8836246
               |
           edu |
High school..  |   -.007694   .2062698    -0.04   0.970    -.4119755    .3965875
 Some college  |  -.1750584   .2113815    -0.83   0.408    -.5893585    .2392418
 College grad  |  -.1918898   .2142556    -0.90   0.370    -.6118231    .2280434
    Post grad  |   .1165934   .2234095     0.52   0.602    -.3212813     .554468
        Other  |  -.7817565   .5188701    -1.51   0.132    -1.798723    .2352101
               |
      vote2016 |
      Clinton  |   .0358048   .0942219     0.38   0.704    -.1488667    .2204762
Other candi..  |   .1295972   .1775493     0.73   0.465     -.218393    .4775873
      No vote  |  -.1340218   .1102528    -1.22   0.224    -.3501134    .0820697
      Not say  |   .1014171   .2155936     0.47   0.638    -.3211386    .5239727
        Other  |   .4415224   .4827597     0.91   0.360    -.5046693    1.387714
               |
         _cons |  -.4194946   .2588283    -1.62   0.105    -.9267887    .0877996
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Equation 4 (excl. 2 variables) (without control variables) - Table A14 (7)
. logit correct numeracy congenial num_con numsq c.numsq#c.congenial incentive in
> _con in_num in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2060.7364  
Iteration 2:   log pseudolikelihood =  -2060.729  
Iteration 3:   log pseudolikelihood =  -2060.729  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(9)  =  31.26
                                                        Prob > chi2   = 0.0003
Log pseudolikelihood = -2060.729                        Pseudo R2     = 0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216312   .0390925    -0.55   0.580    -.0982512    .0549887
   congenial |   .1898645   .0742138     2.56   0.011     .0444081    .3353209
     num_con |   .0644799   .0401015     1.61   0.108    -.0141175    .1430774
       numsq |   .0165344   .0126864     1.30   0.192    -.0083306    .0413994
             |
     c.numsq#|
 c.congenial |   .0014041   .0131991     0.11   0.915    -.0244658    .0272739
             |
   incentive |  -.0049439   .0783185    -0.06   0.950    -.1584453    .1485575
      in_con |  -.1110688   .0794662    -1.40   0.162    -.2668197    .0446822
      in_num |   .0882988    .047539     1.86   0.063    -.0048759    .1814736
  in_num_con |   .0028942   .0483518     0.06   0.952    -.0918736    .0976619
       _cons |  -.3594142   .0728464    -4.93   0.000    -.5021904   -.2166379
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a7

. 
. * Equation 4 (excl. 2 variables) (with control variables) - Table A14 (8)
. logit correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive i
> n_con in_num in_num_con age i.gender i.race i.edu i.vote2016, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2048.4852  
Iteration 2:   log pseudolikelihood = -2048.4602  
Iteration 3:   log pseudolikelihood = -2048.4602  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(29) =  54.49
                                                        Prob > chi2   = 0.0028
Log pseudolikelihood = -2048.4602                       Pseudo R2     = 0.0138

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .1840669   .0741951     2.48   0.013     .0386471    .3294866
      numeracy |  -.0302099   .0403167    -0.75   0.454    -.1092291    .0488093
       num_con |   .0579572   .0403767     1.44   0.151    -.0211796     .137094
         numsq |    .016801   .0128226     1.31   0.190    -.0083309    .0419329
               |
       c.numsq#|
   c.congenial |   .0014892   .0132848     0.11   0.911    -.0245485    .0275269
               |
     incentive |  -.0043179   .0786503    -0.05   0.956    -.1584696    .1498338
        in_con |  -.1067639   .0796904    -1.34   0.180    -.2629543    .0494265
        in_num |   .0854612    .048002     1.78   0.075     -.008621    .1795433
    in_num_con |   .0111203   .0487552     0.23   0.820    -.0844382    .1066787
           age |   .0013608   .0024666     0.55   0.581    -.0034737    .0061954
               |
        gender |
         Male  |   .1424161   .0779714     1.83   0.068    -.0104051    .2952372
        Other  |  -.3216419   .8275652    -0.39   0.698     -1.94364    1.300356
      Not say  |   .9473104   .7780435     1.22   0.223    -.5776268    2.472248
               |
          race |
Non-hispani..  |   .1457948   .1753445     0.83   0.406    -.1978741    .4894637
     Hispanic  |   .2255509   .1131996     1.99   0.046     .0036838    .4474181
        Asian  |   .1584974   .1770581     0.90   0.371    -.1885301     .505525
American In..  |  -.1868578   .5606601    -0.33   0.739    -1.285731    .9120159
       Others  |   .0219035   .2462811     0.09   0.929    -.4607987    .5046056
Prefer not ..  |   .1911684   .3559624     0.54   0.591    -.5065052    .8888419
               |
           edu |
High school..  |  -.0163535   .2067002    -0.08   0.937    -.4214783    .3887714
 Some college  |  -.2018338    .212215    -0.95   0.342    -.6177674    .2140999
 College grad  |   -.218649   .2159077    -1.01   0.311    -.6418204    .2045224
    Post grad  |   .0557334   .2254927     0.25   0.805    -.3862243    .4976911
        Other  |  -.7798163    .516065    -1.51   0.131    -1.791285    .2316525
               |
      vote2016 |
      Clinton  |   .0136762   .0949334     0.14   0.885    -.1723899    .1997423
Other candi..  |   .0854962    .179809     0.48   0.634     -.266923    .4379153
      No vote  |   -.152138   .1107469    -1.37   0.170    -.3691979    .0649219
      Not say  |   .0771176   .2171611     0.36   0.723    -.3485102    .5027455
        Other  |   .4881685   .4778398     1.02   0.307    -.4483804    1.424717
               |
         _cons |  -.4175952    .262802    -1.59   0.112    -.9326777    .0974873
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a8

. 
. * Equation 4 (without control variables) - Table A14 (9)
. logit correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive i
> n_con in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2060.3642  
Iteration 2:   log pseudolikelihood = -2060.3582  
Iteration 3:   log pseudolikelihood = -2060.3582  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(11) =  31.72
                                                        Prob > chi2   = 0.0008
Log pseudolikelihood = -2060.3582                       Pseudo R2     = 0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
             |
     c.numsq#|
 c.congenial |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
             |
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a9

. 
. * Equation 4 (with control variables) - Table A14 (10)
. logit correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive i
> n_con in_num in_numsq in_num_con in_numsq_con age i.gender i.race i.edu i.vote2
> 016, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2048.1684  
Iteration 2:   log pseudolikelihood = -2048.1445  
Iteration 3:   log pseudolikelihood = -2048.1445  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(31) =  54.95
                                                        Prob > chi2   = 0.0051
Log pseudolikelihood = -2048.1445                       Pseudo R2     = 0.0139

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .2248587   .0908694     2.47   0.013      .046758    .4029594
      numeracy |  -.0318067   .0407496    -0.78   0.435    -.1116745     .048061
       num_con |   .0656027   .0409243     1.60   0.109    -.0146074    .1458129
         numsq |   .0198302   .0221264     0.90   0.370    -.0235367    .0631972
               |
       c.numsq#|
   c.congenial |  -.0133599   .0231851    -0.58   0.564    -.0588019     .032082
               |
     incentive |   .0070201   .1079897     0.07   0.948    -.2046358    .2186759
        in_con |   -.166733   .1107172    -1.51   0.132    -.3837346    .0502687
        in_num |   .0878683   .0493091     1.78   0.075    -.0087757    .1845123
      in_numsq |  -.0044369   .0271028    -0.16   0.870    -.0575574    .0486837
    in_num_con |  -.0004179   .0502929    -0.01   0.993    -.0989901    .0981543
  in_numsq_con |   .0217108   .0282759     0.77   0.443     -.033709    .0771305
           age |   .0014092   .0024684     0.57   0.568    -.0034287    .0062471
               |
        gender |
         Male  |   .1405233   .0780786     1.80   0.072     -.012508    .2935546
        Other  |  -.3186339   .8284543    -0.38   0.701    -1.942374    1.305107
      Not say  |   .9550705   .7757067     1.23   0.218    -.5652867    2.475428
               |
          race |
Non-hispani..  |   .1462553   .1751746     0.83   0.404    -.1970806    .4895911
     Hispanic  |   .2243998   .1133691     1.98   0.048     .0022004    .4465991
        Asian  |   .1596958   .1771735     0.90   0.367    -.1875579    .5069494
American In..  |  -.1945383   .5618268    -0.35   0.729    -1.295699     .906622
       Others  |   .0179998   .2460301     0.07   0.942    -.4642103    .5002098
Prefer not ..  |   .1917491   .3555879     0.54   0.590    -.5051903    .8886886
               |
           edu |
High school..  |  -.0185452   .2066092    -0.09   0.928    -.4234918    .3864014
 Some college  |  -.2021779   .2121352    -0.95   0.341    -.6179552    .2135994
 College grad  |   -.220702   .2158266    -1.02   0.307    -.6437144    .2023103
    Post grad  |   .0553266   .2254125     0.25   0.806    -.3864739     .497127
        Other  |  -.7847781   .5177913    -1.52   0.130     -1.79963    .2300741
               |
      vote2016 |
      Clinton  |   .0120057   .0949946     0.13   0.899    -.1741803    .1981916
Other candi..  |   .0841011   .1796975     0.47   0.640    -.2680994    .4363017
      No vote  |  -.1522228   .1107808    -1.37   0.169    -.3693492    .0649037
      Not say  |   .0746915   .2171974     0.34   0.731    -.3510076    .5003906
        Other  |   .4996865   .4778521     1.05   0.296    -.4368865    1.436259
               |
         _cons |  -.4248429   .2673605    -1.59   0.112    -.9488598     .099174
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a10

. 
. * Export Table A14 in Latex
. esttab  a5 a6 a7 a8 a9 a10 using "${main_appendix}/Table_A14.tex",  ///
>                 eqlabel(none) nonumbers mtitles("(5)" "(6)" "(7)" "(8)" "(9)" "
> (10)") b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Logit regression with heterscedasticity robu
> st standard errors." "Control variables in the regression are age, gender, race
> , education, and voting2016")                                     
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A14.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Order effects
. * Table A15: Dependent variable is Numeracy
. * Table A16: Dependent variable is Correct
. * Table A17: Testing for hypotheses 1 and 2 controlling for order effects
. * Table A18: Testing for hypothesis 3 and 4 controlling for order effects
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A15: Dependent variable is Numeracy
. *------------------------------------------------------------------------------
> -
. reg num order_num_treat, r

Linear regression                               Number of obs     =      3,050
                                                F(1, 3048)        =       0.47
                                                Prob > F          =     0.4910
                                                R-squared         =     0.0002
                                                Root MSE          =      1.654

--------------------------------------------------------------------------------
               |               Robust
           num | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |  -.0412564    .059894    -0.69   0.491    -.1586931    .0761803
         _cons |    2.71887   .0422144    64.41   0.000     2.636099    2.801642
--------------------------------------------------------------------------------

. est store a1

.  
. reg num order_num_treat if incentive == 0, r

Linear regression                               Number of obs     =      1,016
                                                F(1, 1014)        =       0.21
                                                Prob > F          =     0.6471
                                                R-squared         =     0.0002
                                                Root MSE          =     1.6566

--------------------------------------------------------------------------------
               |               Robust
           num | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |  -.0475958   .1039268    -0.46   0.647     -.251532    .1563405
         _cons |   2.697495   .0733281    36.79   0.000     2.553603    2.841387
--------------------------------------------------------------------------------

. est store a2

.  
. reg num order_num_treat if incentive ==1, r

Linear regression                               Number of obs     =      2,034
                                                F(1, 2032)        =       0.27
                                                Prob > F          =     0.6035
                                                R-squared         =     0.0001
                                                Root MSE          =     1.6535

--------------------------------------------------------------------------------
               |               Robust
           num | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |  -.0380904   .0733186    -0.52   0.603    -.1818779    .1056972
         _cons |   2.729548   .0516498    52.85   0.000     2.628256     2.83084
--------------------------------------------------------------------------------

. est store a3

. 
. * Export Table A15 in Latex
. esttab a1 a2 a3 using "${main_appendix}/Table_A15.tex",                        
>  ///
>                 nonumbers  b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Randomized order effect: Num) replace                    
>          ///
>                 mtitle("Total" "Non-incentivized" "Incentivized")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A15.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A16: Dependent variable is Correct
. *------------------------------------------------------------------------------
> -
. reg correct order_num_treat, r

Linear regression                               Number of obs     =      3,050
                                                F(1, 3048)        =      14.55
                                                Prob > F          =     0.0001
                                                R-squared         =     0.0048
                                                Root MSE          =     .49291

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0681444   .0178629     3.81   0.000     .0331197     .103169
         _cons |   .3889602   .0123551    31.48   0.000      .364735    .4131854
--------------------------------------------------------------------------------

. est store a4

.  
. reg correct order_num_treat if incentive ==1, r

Linear regression                               Number of obs     =      2,034
                                                F(1, 2032)        =       8.96
                                                Prob > F          =     0.0028
                                                R-squared         =     0.0044
                                                Root MSE          =     .49301

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0654785   .0218779     2.99   0.003      .022573     .108384
         _cons |   .3897979   .0151378    25.75   0.000     .3601107    .4194851
--------------------------------------------------------------------------------

. est store a5

.  
. reg correct order_num_treat if incentive == 0, r

Linear regression                               Number of obs     =      1,016
                                                F(1, 1014)        =       5.63
                                                Prob > F          =     0.0178
                                                R-squared         =     0.0055
                                                Root MSE          =     .49319

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0734814   .0309681     2.37   0.018     .0127124    .1342503
         _cons |   .3872832   .0214037    18.09   0.000     .3452827    .4292838
--------------------------------------------------------------------------------

. est store a6

. 
. * Export Table A16 in Latex 
. esttab a4 a6 a5 using "${main_appendix}/Table_A16.tex",                        
>  ///
>                 nonumbers  b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Randomized order effect: Correct) replace                
>          ///
>                 mtitle("Total" "Non-incentivized" "Incentivized")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A16.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -                
. * Table A17: Testing for hypotheses 1 and 2 controlling for order effects
. *------------------------------------------------------------------------------
> -
. * Adjust the label values to accomodate the table
. label var correct "Correct"

. label var incentive "Incentive"

. label var congenial "Congenial"

. label var numeracy "Numeracy"

. label var numsq "Numeracy$^2$"

. label var num_con "Numeracy $\times$ Congenial"

. label var in_num_con "Incentive $\times$ Numeracy $\times$ Congenial"

. label var in_con "Incentive $\times$ Congenial"

. label var in_num "Incentive $\times$ Numeracy"

. label var in_numsq "Incentive $\times$ Numeracy$^2$"

. label var in_numsq_con "Incentive $\times$ Numeracy$^2$ $\times$ Congenial"

. 
. * Equation 1 (without control variables) - Table A17 (1)
. reg correct order_num_treat congenial numeracy numsq if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(4, 1011)        =       4.10
                                                Prob > F          =     0.0027
                                                R-squared         =     0.0154
                                                Root MSE          =     .49147

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0743238   .0308736     2.41   0.016     .0137401    .1349075
     congenial |   .0479632    .015441     3.11   0.002     .0176632    .0782633
      numeracy |  -.0038624   .0096559    -0.40   0.689    -.0228102    .0150855
         numsq |   .0033869   .0053488     0.63   0.527    -.0071092     .013883
         _cons |    .377127   .0257739    14.63   0.000     .3265506    .4277035
--------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A17 (2)
. reg correct order_num_treat congenial numeracy numsq age i.gender i.race i.edu 
> i.vote2016 if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(24, 991)        =       2.01
                                                Prob > F          =     0.0028
                                                R-squared         =     0.0420
                                                Root MSE          =     .48965

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0702591   .0311252     2.26   0.024     .0091802     .131338
     congenial |   .0445342   .0155864     2.86   0.004      .013948    .0751204
      numeracy |  -.0056061   .0104546    -0.54   0.592    -.0261218    .0149096
         numsq |   .0047267   .0054259     0.87   0.384    -.0059209    .0153743
           age |   .0012628   .0010253     1.23   0.218    -.0007491    .0032748
               |
        gender |
         Male  |   .0320099   .0331578     0.97   0.335    -.0330577    .0970775
        Other  |   .0629558   .3203608     0.20   0.844    -.5657077    .6916193
      Not say  |  -.0533626   .3617293    -0.15   0.883     -.763206    .6564808
               |
          race |
Non-hispani..  |   .0875637    .076163     1.15   0.251    -.0618955     .237023
     Hispanic  |   .1351705   .0458964     2.95   0.003     .0451052    .2252358
        Asian  |   .1516331   .0773862     1.96   0.050    -.0002265    .3034927
American In..  |  -.1801986    .164883    -1.09   0.275    -.5037586    .1433613
       Others  |   .0751437   .0999906     0.75   0.453    -.1210738    .2713613
Prefer not ..  |   .1970266   .1554661     1.27   0.205    -.1080539    .5021071
               |
           edu |
High school..  |  -.0496803   .0798591    -0.62   0.534    -.2063926     .107032
 Some college  |  -.1181144   .0816364    -1.45   0.148    -.2783145    .0420858
 College grad  |  -.1163918   .0834894    -1.39   0.164    -.2802281    .0474445
    Post grad  |  -.0397299   .0882194    -0.45   0.653    -.2128481    .1333884
        Other  |  -.2303411   .1685507    -1.37   0.172    -.5610984    .1004162
               |
      vote2016 |
      Clinton  |  -.0413488   .0398244    -1.04   0.299    -.1194987     .036801
Other candi..  |   .0719417   .0765411     0.94   0.347    -.0782596     .222143
      No vote  |  -.0621073   .0461552    -1.35   0.179    -.1526803    .0284658
      Not say  |   .0686767   .0927701     0.74   0.459    -.1133718    .2507251
        Other  |   .0133723   .1780571     0.08   0.940      -.33604    .3627846
               |
         _cons |   .3625815   .1042412     3.48   0.001     .1580227    .5671403
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Equation 2 (without control variables) - Table A17 (3)
. reg correct order_num_treat congenial numeracy numsq num_con c.numsq#c.congenia
> l  if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(6, 1009)        =       3.47
                                                Prob > F          =     0.0021
                                                R-squared         =     0.0189
                                                Root MSE          =     .49106

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0777581   .0308977     2.52   0.012     .0171269    .1383892
     congenial |   .0581018   .0214578     2.71   0.007     .0159948    .1002088
      numeracy |  -.0045493   .0096204    -0.47   0.636    -.0234275    .0143289
         numsq |    .003735   .0053297     0.70   0.484    -.0067236    .0141936
       num_con |   .0187261   .0098129     1.91   0.057    -.0005299    .0379821
               |
       c.numsq#|
   c.congenial |  -.0041257    .005495    -0.75   0.453    -.0149087    .0066574
               |
         _cons |   .3751017   .0257713    14.55   0.000     .3245301    .4256733
--------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table A17 (4)
. reg correct order_num_treat congenial numeracy numsq num_con c.numsq#c.congenia
> l age i.gender i.race i.edu i.vote2016 if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(26, 989)        =       1.98
                                                Prob > F          =     0.0025
                                                R-squared         =     0.0445
                                                Root MSE          =     .48949

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0736294   .0311614     2.36   0.018     .0124793    .1347794
     congenial |   .0534369   .0215181     2.48   0.013     .0112105    .0956632
      numeracy |  -.0062925   .0104164    -0.60   0.546    -.0267334    .0141483
         numsq |    .005028   .0054058     0.93   0.353    -.0055802    .0156361
       num_con |   .0159907    .009934     1.61   0.108    -.0035033    .0354848
               |
       c.numsq#|
   c.congenial |  -.0035687   .0055428    -0.64   0.520    -.0144456    .0073082
               |
           age |   .0012803   .0010243     1.25   0.212    -.0007298    .0032904
               |
        gender |
         Male  |   .0313983   .0331661     0.95   0.344    -.0336857    .0964824
        Other  |   .0489525   .3149257     0.16   0.877    -.5690467    .6669518
      Not say  |  -.0629899   .3553031    -0.18   0.859    -.7602244    .6342446
               |
          race |
Non-hispani..  |   .0789341   .0759924     1.04   0.299    -.0701909     .228059
     Hispanic  |   .1323228   .0459403     2.88   0.004     .0421711    .2224744
        Asian  |   .1457763   .0776015     1.88   0.061    -.0065062    .2980588
American In..  |  -.1957154    .169338    -1.16   0.248    -.5280184    .1365876
       Others  |   .0711185   .0999692     0.71   0.477    -.1250576    .2672946
Prefer not ..  |   .2020407   .1545984     1.31   0.192    -.1013379    .5054194
               |
           edu |
High school..  |  -.0510144   .0794265    -0.64   0.521    -.2068781    .1048493
 Some college  |  -.1173228   .0811948    -1.44   0.149    -.2766566    .0420111
 College grad  |  -.1141247   .0829517    -1.38   0.169    -.2769063    .0486569
    Post grad  |  -.0414739    .087762    -0.47   0.637    -.2136951    .1307474
        Other  |  -.2329982   .1732384    -1.34   0.179    -.5729552    .1069589
               |
      vote2016 |
      Clinton  |   -.043625   .0399136    -1.09   0.275    -.1219501    .0347001
Other candi..  |     .06567   .0766132     0.86   0.392     -.084673     .216013
      No vote  |  -.0619801   .0460508    -1.35   0.179    -.1523485    .0283883
      Not say  |   .0665571    .093166     0.71   0.475    -.1162687    .2493828
        Other  |   .0170449   .1811095     0.09   0.925    -.3383581    .3724479
               |
         _cons |   .3623126   .1039119     3.49   0.001     .1583994    .5662258
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Export Table A17 in Latex 
. esttab  a1 a2 a3 a4 using "${main_appendix}/Table_A17.tex",  ///
>                 nonumbers mtitles("(1)" "(2)" "(3)" "(4)") b(3) star(* 0.10 ** 
> 0.05  *** 0.01) se(3) ar2  label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A17.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -                
. * Table A18: Testing for hypothesis 3 and 4 controlling for order effects
. *------------------------------------------------------------------------------
> -
. * Equation 3 (without control variables) - Table A18 (5)
. reg correct order_num_treat incentive, r

Linear regression                               Number of obs     =      3,050
                                                F(2, 3047)        =       7.28
                                                Prob > F          =     0.0007
                                                R-squared         =     0.0048
                                                Root MSE          =     .49299

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0681444   .0178658     3.81   0.000      .033114    .1031747
     incentive |  -.0014002   .0189387    -0.07   0.941    -.0385341    .0357337
         _cons |   .3898939   .0176627    22.07   0.000      .355262    .4245259
--------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A18 (6)
. reg correct order_num_treat incentive age i.gender i.race i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(22, 3027)       =       2.02
                                                Prob > F          =     0.0033
                                                R-squared         =     0.0139
                                                Root MSE          =     .49235

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0678231   .0178657     3.80   0.000     .0327929    .1028533
     incentive |  -.0018878   .0188955    -0.10   0.920    -.0389371    .0351615
           age |   .0003405   .0005945     0.57   0.567    -.0008251    .0015061
               |
        gender |
         Male  |   .0383103   .0185529     2.06   0.039     .0019329    .0746878
        Other  |  -.0826508   .1767955    -0.47   0.640    -.4293022    .2640006
      Not say  |   .2320643   .1701847     1.36   0.173     -.101625    .5657535
               |
          race |
Non-hispani..  |   .0332695    .042116     0.79   0.430    -.0493094    .1158484
     Hispanic  |   .0533131   .0275708     1.93   0.053    -.0007462    .1073724
        Asian  |   .0401164   .0426382     0.94   0.347    -.0434863    .1237191
American In..  |  -.0224677   .1248687    -0.18   0.857    -.2673037    .2223683
       Others  |   .0002711   .0590783     0.00   0.996    -.1155665    .1161088
Prefer not ..  |   .0380827   .0867536     0.44   0.661    -.1320191    .2081846
               |
           edu |
High school..  |  -.0043015   .0500258    -0.09   0.931    -.1023896    .0937866
 Some college  |  -.0427977   .0511245    -0.84   0.403      -.14304    .0574447
 College grad  |  -.0457346    .051909    -0.88   0.378     -.147515    .0560459
    Post grad  |   .0300355   .0544129     0.55   0.581    -.0766545    .1367256
        Other  |  -.1759522   .1049314    -1.68   0.094    -.3816962    .0297917
               |
      vote2016 |
      Clinton  |    .008516   .0229347     0.37   0.710    -.0364531    .0534852
Other candi..  |   .0329675   .0434998     0.76   0.449    -.0523247    .1182596
      No vote  |  -.0318398   .0265273    -1.20   0.230    -.0838531    .0201735
      Not say  |   .0289368   .0527689     0.55   0.583    -.0745298    .1324035
        Other  |   .1140752   .1186603     0.96   0.336    -.1185878    .3467381
               |
         _cons |    .365001   .0632652     5.77   0.000      .240954     .489048
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Equation 4 (excl. 2 variables) (without control variables) - Table A18 (7)
. reg correct order_num_treat numeracy congenial num_con numsq c.numsq#c.congenia
> l incentive in_con in_num in_num_con, r

Linear regression                               Number of obs     =      3,050
                                                F(10, 3039)       =       4.99
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0158
                                                Root MSE          =      .4909

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0701128   .0178209     3.93   0.000     .0351706    .1050551
      numeracy |  -.0045853   .0094128    -0.49   0.626    -.0230414    .0138708
     congenial |   .0472305   .0176172     2.68   0.007     .0126877    .0817734
       num_con |   .0164549   .0094631     1.74   0.082    -.0020998    .0350095
         numsq |   .0042638   .0030562     1.40   0.163    -.0017285    .0102562
               |
       c.numsq#|
   c.congenial |  -.0001862    .003135    -0.06   0.953    -.0063332    .0059608
               |
     incentive |  -.0018101    .018846    -0.10   0.923    -.0387622     .035142
        in_con |  -.0265629   .0189125    -1.40   0.160    -.0636455    .0105197
        in_num |   .0211055   .0114255     1.85   0.065     -.001297    .0435081
    in_num_con |   .0005008   .0113767     0.04   0.965    -.0218061    .0228076
         _cons |   .3772085   .0194176    19.43   0.000     .3391356    .4152814
--------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a7

. 
. * Equation 4 (excl. 2 variables) (with control variables) - Table A18 (8)
. reg correct order_num_treat congenial numeracy num_con numsq c.numsq#c.congenia
> l incentive in_con in_num in_num_con age i.gender i.race i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(30, 3019)       =       2.54
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0236
                                                Root MSE          =     .49056

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0694749   .0178293     3.90   0.000     .0345161    .1044337
     congenial |   .0455019   .0175674     2.59   0.010     .0110565    .0799473
      numeracy |  -.0067212    .009654    -0.70   0.486    -.0256502    .0122079
       num_con |   .0147429    .009497     1.55   0.121    -.0038783    .0333641
         numsq |   .0043063   .0030742     1.40   0.161    -.0017214    .0103341
               |
       c.numsq#|
   c.congenial |  -.0001743   .0031462    -0.06   0.956    -.0063431    .0059946
               |
     incentive |  -.0018139   .0188184    -0.10   0.923    -.0387122    .0350843
        in_con |  -.0252424   .0189155    -1.33   0.182     -.062331    .0118462
        in_num |   .0202431   .0114757     1.76   0.078    -.0022579    .0427441
    in_num_con |   .0025259    .011435     0.22   0.825    -.0198953    .0249471
           age |   .0003276   .0005925     0.55   0.580    -.0008342    .0014893
               |
        gender |
         Male  |   .0327546   .0187433     1.75   0.081    -.0039964    .0695056
        Other  |  -.0845419   .1730602    -0.49   0.625    -.4238696    .2547859
      Not say  |   .2348196   .1718462     1.37   0.172    -.1021278     .571767
               |
          race |
Non-hispani..  |   .0350644   .0428448     0.82   0.413    -.0489436    .1190724
     Hispanic  |   .0524989   .0274906     1.91   0.056    -.0014033    .1064011
        Asian  |   .0363019   .0427543     0.85   0.396    -.0475286    .1201324
American In..  |  -.0350287   .1281278    -0.27   0.785    -.2862554     .216198
       Others  |   .0017543   .0581878     0.03   0.976    -.1123374    .1158461
Prefer not ..  |   .0384886   .0868008     0.44   0.657     -.131706    .2086833
               |
           edu |
High school..  |  -.0064358   .0500651    -0.13   0.898    -.1046008    .0917293
 Some college  |  -.0490102   .0512277    -0.96   0.339    -.1494549    .0514345
 College grad  |  -.0516242   .0521814    -0.99   0.323    -.1539389    .0506905
    Post grad  |   .0147265   .0547517     0.27   0.788    -.0926278    .1220809
        Other  |  -.1748735   .1038277    -1.68   0.092    -.3784537    .0287066
               |
      vote2016 |
      Clinton  |   .0028935   .0228652     0.13   0.899    -.0419393    .0477264
Other candi..  |   .0212714   .0437069     0.49   0.627    -.0644269    .1069697
      No vote  |  -.0364782    .026467    -1.38   0.168    -.0883734    .0154171
      Not say  |   .0226238    .052942     0.43   0.669    -.0811822    .1264299
        Other  |   .1242433   .1176704     1.06   0.291     -.106479    .3549656
               |
         _cons |    .365579    .063982     5.71   0.000     .2401263    .4910317
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a8

. 
. * Equation 4 (without control variables) - Table A18 (9)
. reg correct order_num_treat congenial numeracy num_con numsq c.numsq#c.congenia
> l incentive in_con in_num in_numsq in_num_con in_numsq_con, r

Linear regression                               Number of obs     =      3,050
                                                F(12, 3037)       =       4.22
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0160
                                                Root MSE          =       .491

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0701076   .0178245     3.93   0.000     .0351582    .1050569
     congenial |   .0579155    .021437     2.70   0.007     .0158829     .099948
      numeracy |  -.0045695   .0096044    -0.48   0.634    -.0234013    .0142623
       num_con |   .0185911   .0097903     1.90   0.058    -.0006052    .0377875
         numsq |   .0037163   .0053217     0.70   0.485    -.0067183    .0141509
               |
       c.numsq#|
   c.congenial |  -.0040657   .0054815    -0.74   0.458    -.0148136    .0066822
               |
     incentive |  -.0042204   .0258501    -0.16   0.870    -.0549058     .046465
        in_con |  -.0423679   .0262243    -1.62   0.106    -.0937872    .0090514
        in_num |   .0209578   .0118328     1.77   0.077    -.0022433     .044159
      in_numsq |   .0007711   .0065007     0.12   0.906    -.0119752    .0135173
    in_num_con |  -.0026896   .0120098    -0.22   0.823    -.0262377    .0208584
  in_numsq_con |   .0056881   .0066764     0.85   0.394    -.0074026    .0187787
         _cons |   .3788896   .0227785    16.63   0.000     .3342267    .4235525
--------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a9

. 
. * Equation 4 (without control variables) - Table A18 (10)
. reg correct order_num_treat congenial numeracy num_con numsq c.numsq#c.congenia
> l incentive in_con in_num in_numsq in_num_con in_numsq_con age i.gender i.race 
> i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(32, 3017)       =       2.40
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0238
                                                Root MSE          =     .49067

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
order_num_tr~t |   .0694955   .0178335     3.90   0.000     .0345285    .1044625
     congenial |   .0553495   .0212827     2.60   0.009     .0136194    .0970796
      numeracy |  -.0071733   .0098442    -0.73   0.466    -.0264754    .0121288
       num_con |   .0167888   .0098232     1.71   0.088    -.0024721    .0360496
         numsq |   .0049118   .0053221     0.92   0.356    -.0055236    .0153471
               |
       c.numsq#|
   c.congenial |  -.0037664   .0054681    -0.69   0.491     -.014488    .0069552
               |
     incentive |   .0004928   .0257805     0.02   0.985    -.0500563    .0510419
        in_con |  -.0398435   .0261251    -1.53   0.127    -.0910684    .0113813
        in_num |   .0208916   .0118766     1.76   0.079    -.0023955    .0441787
      in_numsq |  -.0009452   .0065111    -0.15   0.885    -.0137118    .0118214
    in_num_con |  -.0005017   .0120569    -0.04   0.967    -.0241423    .0231388
  in_numsq_con |   .0052846   .0066824     0.79   0.429    -.0078179    .0183872
           age |   .0003394   .0005931     0.57   0.567    -.0008235    .0015022
               |
        gender |
         Male  |   .0322764   .0187698     1.72   0.086    -.0045266    .0690794
        Other  |  -.0839598   .1733803    -0.48   0.628    -.4239154    .2559957
      Not say  |   .2366191   .1711922     1.38   0.167     -.099046    .5722843
               |
          race |
Non-hispani..  |   .0351635   .0428108     0.82   0.412    -.0487777    .1191048
     Hispanic  |   .0522057   .0275304     1.90   0.058    -.0017745     .106186
        Asian  |   .0366351   .0428056     0.86   0.392    -.0472961    .1205663
American In..  |  -.0369718   .1284407    -0.29   0.773     -.288812    .2148684
       Others  |   .0008257   .0581291     0.01   0.989     -.113151    .1148024
Prefer not ..  |   .0386209   .0867066     0.45   0.656     -.131389    .2086309
               |
           edu |
High school..  |   -.006946   .0500683    -0.14   0.890    -.1051173    .0912254
 Some college  |  -.0490485     .05123    -0.96   0.338    -.1494977    .0514007
 College grad  |  -.0520902   .0521829    -1.00   0.318    -.1544079    .0502275
    Post grad  |    .014648   .0547538     0.27   0.789    -.0927106    .1220065
        Other  |  -.1756877   .1041691    -1.69   0.092    -.3799374    .0285619
               |
      vote2016 |
      Clinton  |   .0024716   .0228818     0.11   0.914     -.042394    .0473372
Other candi..  |   .0208961   .0436849     0.48   0.632    -.0647591    .1065513
      No vote  |  -.0365022   .0264823    -1.38   0.168    -.0884273    .0154229
      Not say  |   .0220058   .0529477     0.42   0.678    -.0818114     .125823
        Other  |   .1269957   .1176711     1.08   0.281     -.103728    .3577195
               |
         _cons |    .364191   .0650876     5.60   0.000     .2365706    .4918115
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a10

. 
. * Export Table A18 in Latex 
. 
. esttab  a5 a6 a7 a8 a9 a10 using "${main_appendix}/Table_A18.tex" ,  ///
>                 nonumbers mtitles("(5)" "(6)" "(7)" "(8)" "(9)" "(10)") b(3) st
> ar(* 0.10 ** 0.05  *** 0.01) se(3) ar2 label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A18.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Split sample analyses - Numeracy *AFTER* treatment
. * Table A19: The impact of numeracy and congeniality on accuracy
. * Table A20: The impact of incentive, numeracy, and congeniality on accuracy
. * Figure A1: Predicted probabilities of correctly interpreting the data (-1,0,1
> SD)
. * Figure A2: Predicted probabilities of correctly interpreting the data (2SD)
. * Table A21: Differences in the predicted congeneity bias
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A19: The impact of numeracy and congeniality on accuracy
. *------------------------------------------------------------------------------
> -
. * Numeracy is measured after (order_num_treat == 0)
. * Equation 1 (without control variables) - Table A19 (1)
. reg correct congenial numeracy numsq if incentive==0 & order_num_treat==0, r

Linear regression                               Number of obs     =        519
                                                F(3, 515)         =       5.81
                                                Prob > F          =     0.0007
                                                R-squared         =     0.0313
                                                Root MSE          =     .48129

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0804263   .0208972     3.85   0.000      .039372    .1214806
    numeracy |  -.0191874   .0131961    -1.45   0.147    -.0451123    .0067375
       numsq |   .0083616   .0072898     1.15   0.252    -.0059599    .0226831
       _cons |   .3627673   .0291331    12.45   0.000     .3055329    .4200017
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A19 (2)
. reg correct congenial numeracy numsq age i.gender i.race i.edu i.vote2016 if in
> centive==0 & order_num_treat==0, r

Linear regression                               Number of obs     =        519
                                                F(22, 496)        =       2.74
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0873
                                                Root MSE          =     .47605

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0736273   .0210712     3.49   0.001     .0322275    .1150272
      numeracy |  -.0148406    .014462    -1.03   0.305    -.0432549    .0135737
         numsq |   .0102568   .0074729     1.37   0.171    -.0044257    .0249393
           age |   .0014735   .0014097     1.05   0.296    -.0012962    .0042432
               |
        gender |
         Male  |  -.0128205   .0454715    -0.28   0.778    -.1021611    .0765201
      Not say  |  -.3095703   .3524555    -0.88   0.380     -1.00206    .3829195
               |
          race |
Non-hispani..  |   .0257898   .1065966     0.24   0.809    -.1836468    .2352264
     Hispanic  |    .237501   .0643682     3.69   0.000     .1110331     .363969
        Asian  |   .0216375   .1044375     0.21   0.836     -.183557    .2268319
American In..  |   .0704157   .2647246     0.27   0.790    -.4497042    .5905356
       Others  |   .1392597   .1365012     1.02   0.308    -.1289322    .4074517
Prefer not ..  |   .4152666   .1446054     2.87   0.004     .1311519    .6993813
               |
           edu |
High school..  |   -.169557   .1228658    -1.38   0.168    -.4109585    .0718445
 Some college  |  -.2580489   .1246509    -2.07   0.039    -.5029579     -.01314
 College grad  |   -.201047   .1252754    -1.60   0.109    -.4471829     .045089
    Post grad  |  -.2075426   .1312527    -1.58   0.114    -.4654223    .0503372
        Other  |  -.4373346   .2112975    -2.07   0.039    -.8524832   -.0221861
               |
      vote2016 |
      Clinton  |  -.0909393   .0537119    -1.69   0.091    -.1964701    .0145916
Other candi..  |  -.0395727   .1074028    -0.37   0.713    -.2505932    .1714478
      No vote  |   -.086388   .0624318    -1.38   0.167    -.2090514    .0362755
      Not say  |   .0463704   .1136956     0.41   0.684     -.177014    .2697547
        Other  |   .0530627   .2031005     0.26   0.794    -.3459807    .4521061
               |
         _cons |   .4888212   .1445793     3.38   0.001     .2047579    .7728845
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Equation 2 (without control variables) - Table A19 (3)
. reg correct congenial numeracy numsq num_con c.numsq#c.congenial  if incentive=
> =0 & order_num_treat==0, r

Linear regression                               Number of obs     =        519
                                                F(5, 513)         =       3.97
                                                Prob > F          =     0.0015
                                                R-squared         =     0.0342
                                                Root MSE          =     .48152

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0661167   .0293045     2.26   0.024     .0085451    .1236883
    numeracy |  -.0192978   .0132106    -1.46   0.145    -.0452513    .0066557
       numsq |   .0084282   .0072765     1.16   0.247    -.0058672    .0227236
     num_con |   .0106008   .0131992     0.80   0.422    -.0153303     .036532
             |
     c.numsq#|
 c.congenial |   .0048683   .0073604     0.66   0.509     -.009592    .0193286
             |
       _cons |   .3623699   .0291691    12.42   0.000     .3050643    .4196756
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (without control variables) - Table A19 (4)
. reg correct congenial numeracy numsq num_con c.numsq#c.congenial age i.gender i
> .race i.edu i.vote2016 if incentive==0 & order_num_treat==0, r

Linear regression                               Number of obs     =        519
                                                F(24, 494)        =       2.59
                                                Prob > F          =     0.0001
                                                R-squared         =     0.0915
                                                Root MSE          =     .47592

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0511645   .0295528     1.73   0.084    -.0069002    .1092291
      numeracy |  -.0150185   .0144652    -1.04   0.300    -.0434395    .0134025
         numsq |   .0104271   .0074628     1.40   0.163    -.0042356    .0250898
       num_con |   .0092343   .0133453     0.69   0.489    -.0169863    .0354548
               |
       c.numsq#|
   c.congenial |    .007888    .007464     1.06   0.291    -.0067771    .0225531
               |
           age |   .0014389   .0014048     1.02   0.306    -.0013212     .004199
               |
        gender |
         Male  |  -.0116715   .0454881    -0.26   0.798    -.1010456    .0777026
      Not say  |  -.3237602   .3445164    -0.94   0.348    -1.000658     .353138
               |
          race |
Non-hispani..  |   .0279009   .1066005     0.26   0.794    -.1815453    .2373472
     Hispanic  |   .2431539   .0646113     3.76   0.000      .116207    .3701008
        Asian  |    .012169   .1056807     0.12   0.908    -.1954702    .2198082
American In..  |   .0570602   .2716509     0.21   0.834    -.4766735    .5907939
       Others  |   .1396169   .1360965     1.03   0.305    -.1277826    .4070163
Prefer not ..  |   .4184733   .1451614     2.88   0.004     .1332633    .7036832
               |
           edu |
High school..  |  -.1671307   .1218641    -1.37   0.171    -.4065665    .0723052
 Some college  |  -.2537903   .1238755    -2.05   0.041     -.497178   -.0104025
 College grad  |  -.1925284   .1245408    -1.55   0.123    -.4372234    .0521667
    Post grad  |   -.204522   .1302585    -1.57   0.117     -.460451     .051407
        Other  |  -.4322092   .2129528    -2.03   0.043    -.8506141   -.0138043
               |
      vote2016 |
      Clinton  |  -.0919188   .0538321    -1.71   0.088     -.197687    .0138493
Other candi..  |  -.0387797   .1071896    -0.36   0.718    -.2493836    .1718241
      No vote  |  -.0831881   .0619443    -1.34   0.180     -.204895    .0385188
      Not say  |   .0473447   .1147207     0.41   0.680    -.1780561    .2727455
        Other  |   .0507872   .2035306     0.25   0.803    -.3491052    .4506795
               |
         _cons |    .483733   .1430837     3.38   0.001     .2026054    .7648606
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Export Table A19 in Latex 
. esttab  a1 a2 a3 a4 using "${main_appendix}/Table_A19.tex" ,  ///
>                 nonumbers mtitles("(1)" "(2)" "(3)" "(4)") b(3) star(* 0.10 ** 
> 0.05  *** 0.01) se(3) ar2  label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A19.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A20: The impatc of incentive, numeracy, and congeniality on accuracy
. *------------------------------------------------------------------------------
> -
. * Numeracy is measured after (order_num_treat == 0)
. * Equation 3 (without control variables) - Table A20 (5)
. reg correct incentive if order_num_treat==0, r

Linear regression                               Number of obs     =      1,558
                                                F(1, 1556)        =       0.01
                                                Prob > F          =     0.9236
                                                R-squared         =     0.0000
                                                Root MSE          =     .48783

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |   .0025146   .0262112     0.10   0.924    -.0488983    .0539276
       _cons |   .3872832   .0213963    18.10   0.000     .3453145    .4292519
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A20 (6)
. reg correct incentive age i.gender i.race i.edu i.vote2016 if order_num_treat==
> 0, r

Linear regression                               Number of obs     =      1,558
                                                F(21, 1536)       =       7.64
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0119
                                                Root MSE          =     .48807

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |   .0035837   .0262999     0.14   0.892    -.0480038    .0551712
           age |   .0008039   .0008247     0.97   0.330    -.0008137    .0024216
               |
        gender |
         Male  |   .0407538    .025868     1.58   0.115    -.0099866    .0914942
        Other  |  -.3725424   .0470101    -7.92   0.000    -.4647532   -.2803317
      Not say  |  -.0145234   .2203496    -0.07   0.947    -.4467413    .4176945
               |
          race |
Non-hispani..  |   .0682392   .0592667     1.15   0.250    -.0480131    .1844915
     Hispanic  |   .0865737   .0390181     2.22   0.027     .0100394     .163108
        Asian  |   .0097659   .0601097     0.16   0.871    -.1081398    .1276716
American In..  |  -.0223336   .1566115    -0.14   0.887    -.3295285    .2848613
       Others  |  -.0240193   .0830608    -0.29   0.772    -.1869438    .1389052
Prefer not ..  |   .1193691   .1320683     0.90   0.366    -.1396842    .3784223
               |
           edu |
High school..  |  -.0219854   .0690989    -0.32   0.750    -.1575236    .1135528
 Some college  |  -.0577974   .0708585    -0.82   0.415    -.1967871    .0811922
 College grad  |  -.0339144   .0718897    -0.47   0.637    -.1749267    .1070979
    Post grad  |  -.0019487   .0757945    -0.03   0.979    -.1506203     .146723
        Other  |  -.3517738   .1194287    -2.95   0.003    -.5860344   -.1175132
               |
      vote2016 |
      Clinton  |   .0014403   .0319291     0.05   0.964    -.0611889    .0640695
Other candi..  |  -.0030212   .0594234    -0.05   0.959    -.1195806    .1135383
      No vote  |  -.0090552   .0373282    -0.24   0.808    -.0822748    .0641644
      Not say  |   .0417586   .0706051     0.59   0.554    -.0967339    .1802511
        Other  |   .1269539   .1531725     0.83   0.407    -.1734954    .4274032
               |
         _cons |   .3398299   .0856767     3.97   0.000     .1717743    .5078855
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Equation 4 (excl. 2 variables) (without control variables) - Table A20 (7)
. reg correct numeracy congenial num_con numsq c.numsq#c.congenial incentive in_c
> on in_num in_num_con if order_num_treat==0, r

Linear regression                               Number of obs     =      1,558
                                                F(9, 1548)        =       2.96
                                                Prob > F          =     0.0017
                                                R-squared         =     0.0160
                                                Root MSE          =     .48515

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0181826   .0127794    -1.42   0.155    -.0432493    .0068841
   congenial |   .0711009   .0239725     2.97   0.003     .0240789    .1181229
     num_con |   .0117553   .0126344     0.93   0.352    -.0130271    .0365376
       numsq |   .0061694   .0041816     1.48   0.140    -.0020328    .0143716
             |
     c.numsq#|
 c.congenial |   .0029792   .0042148     0.71   0.480    -.0052881    .0112465
             |
   incentive |   .0038627   .0259196     0.15   0.882    -.0469786     .054704
      in_con |  -.0551946   .0257011    -2.15   0.032    -.1056072    -.004782
      in_num |   .0286658   .0155638     1.84   0.066    -.0018625    .0591941
  in_num_con |   -.003606   .0152831    -0.24   0.814    -.0335837    .0263716
       _cons |   .3685126   .0240212    15.34   0.000      .321395    .4156302
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a7

. 
. * Equation 4 (excl. 2 variables) (with control variables) - Table A20 (8)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_num_con age i.gender i.race i.edu i.vote2016 if order_num_treat==
> 0, r

Linear regression                               Number of obs     =      1,558
                                                F(29, 1528)       =       4.92
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0270
                                                Root MSE          =     .48559

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0684988     .02398     2.86   0.004     .0214617     .115536
      numeracy |  -.0186169   .0131426    -1.42   0.157    -.0443963    .0071625
       num_con |    .010574   .0127055     0.83   0.405    -.0143479     .035496
         numsq |   .0062172   .0042184     1.47   0.141    -.0020574    .0144918
               |
       c.numsq#|
   c.congenial |   .0035903   .0042488     0.85   0.398    -.0047437    .0119244
               |
     incentive |    .005659   .0260017     0.22   0.828    -.0453438    .0566617
        in_con |  -.0553058   .0257619    -2.15   0.032    -.1058382   -.0047734
        in_num |   .0261162   .0157542     1.66   0.098    -.0047859    .0570183
    in_num_con |  -.0023264   .0153831    -0.15   0.880    -.0325006    .0278477
           age |   .0007025   .0008243     0.85   0.394    -.0009144    .0023193
               |
        gender |
         Male  |   .0381878    .026086     1.46   0.143    -.0129804     .089356
        Other  |  -.4098465   .0571329    -7.17   0.000    -.5219138   -.2977793
      Not say  |   -.021561    .219441    -0.10   0.922    -.4519985    .4088764
               |
          race |
Non-hispani..  |   .0660371   .0601152     1.10   0.272    -.0518799     .183954
     Hispanic  |   .0852525   .0387108     2.20   0.028     .0093205    .1611844
        Asian  |   .0097103   .0607889     0.16   0.873    -.1095282    .1289489
American In..  |  -.0228276   .1591747    -0.14   0.886    -.3350515    .2893964
       Others  |  -.0390474   .0808636    -0.48   0.629    -.1976628    .1195681
Prefer not ..  |   .1112249   .1288426     0.86   0.388    -.1415021     .363952
               |
           edu |
High school..  |   -.022619   .0702168    -0.32   0.747    -.1603506    .1151126
 Some college  |  -.0562748   .0719297    -0.78   0.434    -.1973661    .0848165
 College grad  |  -.0341039    .073068    -0.47   0.641     -.177428    .1092203
    Post grad  |  -.0143871   .0770102    -0.19   0.852    -.1654441    .1366698
        Other  |  -.3465216   .1136287    -3.05   0.002    -.5694063   -.1236368
               |
      vote2016 |
      Clinton  |  -.0003644   .0318402    -0.01   0.991    -.0628195    .0620907
Other candi..  |  -.0090426   .0591438    -0.15   0.879    -.1250543    .1069691
      No vote  |  -.0131028   .0371612    -0.35   0.724    -.0859952    .0597896
      Not say  |    .029833   .0702846     0.42   0.671    -.1080315    .1676975
        Other  |   .1407483   .1527739     0.92   0.357    -.1589204     .440417
               |
         _cons |   .3321044   .0865335     3.84   0.000     .1623674    .5018414
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a8

. 
. * Equation 4 (without control variables) - Table A20 (9)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con if order_num_treat==0, r

Linear regression                               Number of obs     =      1,558
                                                F(11, 1546)       =       2.46
                                                Prob > F          =     0.0047
                                                R-squared         =     0.0162
                                                Root MSE          =     .48543

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0661167   .0292475     2.26   0.024     .0087478    .1234856
    numeracy |  -.0192978   .0131849    -1.46   0.143    -.0451599    .0065643
     num_con |   .0106008   .0131735     0.80   0.421     -.015239    .0364407
       numsq |   .0084282   .0072623     1.16   0.246    -.0058169    .0226732
             |
     c.numsq#|
 c.congenial |   .0048683   .0073461     0.66   0.508    -.0095411    .0192777
             |
   incentive |   .0128995   .0356553     0.36   0.718    -.0570383    .0828373
      in_con |   -.048066   .0356826    -1.35   0.178    -.1180574    .0219253
      in_num |   .0303204   .0162622     1.86   0.062     -.001578    .0622188
    in_numsq |  -.0033264   .0088838    -0.37   0.708     -.020752    .0140991
  in_num_con |  -.0020863   .0162372    -0.13   0.898    -.0339355     .029763
in_numsq_con |  -.0026588   .0089602    -0.30   0.767    -.0202341    .0149166
       _cons |   .3623699   .0291124    12.45   0.000      .305266    .4194738
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a9

. 
. * Equation 4 (with control variables) - Table A20 (10)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con age i.gender i.race i.edu i.vote201
> 6 if order_num_treat==0, r

Linear regression                               Number of obs     =      1,558
                                                F(31, 1526)       =       4.00
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0273
                                                Root MSE          =     .48582

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0612447   .0290521     2.11   0.035     .0042584    .1182309
      numeracy |    -.02047   .0135502    -1.51   0.131    -.0470489    .0061089
       num_con |   .0088579   .0132091     0.67   0.503    -.0170519    .0347678
         numsq |   .0099694   .0072752     1.37   0.171     -.004301    .0242398
               |
       c.numsq#|
   c.congenial |   .0063305    .007336     0.86   0.388    -.0080592    .0207201
               |
     incentive |   .0207434    .035641     0.58   0.561    -.0491672    .0906539
        in_con |  -.0450398   .0356048    -1.26   0.206    -.1148794    .0247998
        in_num |   .0288455   .0164345     1.76   0.079    -.0033911    .0610821
      in_numsq |   -.005551   .0089339    -0.62   0.534    -.0230751     .011973
    in_num_con |  -.0000746   .0162768    -0.00   0.996    -.0320018    .0318526
  in_numsq_con |  -.0038397   .0089732    -0.43   0.669    -.0214408    .0137614
           age |    .000713   .0008243     0.86   0.387     -.000904    .0023299
               |
        gender |
         Male  |   .0390134   .0261291     1.49   0.136    -.0122393    .0902661
        Other  |  -.4000616   .0625121    -6.40   0.000    -.5226804   -.2774429
      Not say  |  -.0203546   .2210527    -0.09   0.927    -.4539538    .4132445
               |
          race |
Non-hispani..  |   .0678438   .0601089     1.13   0.259    -.0500609    .1857485
     Hispanic  |   .0877261   .0388087     2.26   0.024      .011602    .1638502
        Asian  |   .0091354   .0608028     0.15   0.881    -.1101306    .1284014
American In..  |  -.0226246   .1589794    -0.14   0.887    -.3344659    .2892167
       Others  |  -.0374791   .0803244    -0.47   0.641     -.195037    .1200789
Prefer not ..  |   .1110701   .1293795     0.86   0.391    -.1427105    .3648506
               |
           edu |
High school..  |  -.0229544    .070474    -0.33   0.745    -.1611906    .1152817
 Some college  |    -.05712   .0721933    -0.79   0.429    -.1987285    .0844885
 College grad  |  -.0354071   .0733535    -0.48   0.629    -.1792914    .1084773
    Post grad  |  -.0144317   .0772405    -0.19   0.852    -.1659405    .1370771
        Other  |  -.3473746    .113632    -3.06   0.002    -.5702661   -.1244832
               |
      vote2016 |
      Clinton  |  -.0002596   .0318497    -0.01   0.993    -.0627334    .0622142
Other candi..  |  -.0090341   .0591501    -0.15   0.879    -.1250582    .1069901
      No vote  |  -.0140424   .0371608    -0.38   0.706    -.0869341    .0588492
      Not say  |   .0294656   .0702075     0.42   0.675    -.1082478    .1671791
        Other  |   .1384405   .1531844     0.90   0.366    -.1620338    .4389148
               |
         _cons |   .3213841   .0881651     3.65   0.000     .1484465    .4943217
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a10

. 
. * Export Table A20 in Latex 
. esttab  a5 a6 a7 a8 a9 a10 using "${main_appendix}/Table_A20.tex" ,  ///
>                 nonumbers mtitles("(5)" "(6)" "(7)" "(8)" "(9)" "(10)") b(3) st
> ar(* 0.10 ** 0.05  *** 0.01) se(3) ar2 label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")                                     
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A20.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A1: Predicted probabilities of correctly interpreting the data (-1,0,1
> SD)
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. * GRAPH1: TOP-LEFT Graph (Non-incentivized & Low numeracy)
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.666, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial -1 num_con 1.666 numsq 2.776 numsq_con -2.776 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3574079     .0428916      .275871    .4475773

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 1 num_con -1.666 numsq 2.776 numsq_con 2.776 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4785889     .0464831     .3880237    .5714267

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 0 num_con 0 numsq 2.776 numsq_con 0 incentive 0 
> in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_treat == 
> 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4174414     .0311959     .3583688    .4782812

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3574079    .0428916   .2202274   .4916125
          p2 |      1,000    .4785889    .0464831   .3216207   .6384096
          p3 |      1,000    .4174414    .0311959   .3114013   .5074872

. 
. *-------------------------------------------------------GRAPH1-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.33 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9.5 0.54 "Congenial = +1", color (green) size(small)))        /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (12 0.48 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("Low numeracy", size (medium))           
>                                                                                
>                                                   ///
>                                 name(topleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH2: TOP-RIGHT Graph (Non-incentivized & High numeracy)
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=+1.666, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial -1 num_con -1.666 numsq 2.776 numsq_con -2.776 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .2545289     .0394659     .1817564    .3407663

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 1 num_con 1.666 numsq 2.776 numsq_con 2.776 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4544304     .0424213     .3736871    .5427779

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 0 num_con 0 numsq 2.776 numsq_con 0 incentive 0 i
> n_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_treat == 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3475707     .0304197     .2899551    .4100978

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .2545289    .0394659   .1604476   .3871232
          p2 |      1,000    .4544304    .0424213   .3198479   .5866172
          p3 |      1,000    .3475707    .0304197   .2696382   .4540719

. 
. *-------------------------------------------------------GRAPH2-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(12 0.26 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(10 0.45 "Congenial = +1", color (green) size(small)))         /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (12.5 0.41 "Congenial = 0", color (gs5) size(small)))            ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("High numeracy", size (medium))          
>                                                                                
>                                                   ///
>                                 name(topright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH3: BOTTOM-LEFT Graph (Incentivized & Low numeracy)
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.666, incentive =1
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial -1 num_con 1.666 numsq 2.776 numsq_con -2.776 in
> centive 1 in_con -1 in_num -1.666 in_numsq 2.776 in_num_con 1.666 in_numsq_con 
> -2.776 if order_num_treat == 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3623241     .0299723     .3062778    .4245729

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 1 num_con -1.666 numsq 2.776 numsq_con 2.776 inc
> entive 1 in_con 1 in_num -1.666 in_numsq 2.776 in_num_con -1.666 in_numsq_con 2
> .776 if order_num_treat == 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3811831     .0315996     .3214167    .4462238

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 0 num_con 0 numsq 2.776 numsq_con 0 incentive 1 
> in_con 0 in_num -1.666 in_numsq 2.776 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3712449     .0209256      .333032    .4122982

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3623241    .0299723   .2677602    .461237
          p2 |      1,000    .3811831    .0315996   .2681192   .4875695
          p3 |      1,000    .3712449    .0209256   .2907535   .4565938

. *-------------------------------------------------------GRAPH3-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(12 0.29 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.47 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (16 0.44 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("  Incentivized  ", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH4: BOTTOM-RIGHT Graph (Incentivized & High numeracy)
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs.*/
. * High Numeracy, Incentive=1*/
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=1.666, incentive =1*/
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial -1 num_con -1.666 numsq 2.776 numsq_con -2.776 in
> centive 1 in_con -1 in_num 1.666 in_numsq 2.776 in_num_con -1.666 in_numsq_con 
> -2.776 if order_num_treat == 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3693982     .0301376     .3106085    .4310265

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 1 num_con 1.666 numsq 2.776 numsq_con 2.776 incen
> tive 1 in_con 1 in_num 1.666 in_numsq 2.776 in_num_con 1.666 in_numsq_con 2.776
>  if order_num_treat == 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4467384     .0307458     .3888425    .5074576

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 0 num_con 0 numsq 2.776 numsq_con 0 incentive 1 i
> n_con 0 in_num 1.666 in_numsq 2.776 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4071473     .0220197     .3648062     .450266

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3693982    .0301376   .2891984   .4672492
          p2 |      1,000    .4467384    .0307458   .3508368   .5361108
          p3 |      1,000    .4071473    .0220197     .34378   .4687055

. *-------------------------------------------------------GRAPH4-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.29 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(14 0.48 "Congenial = +1", color (green) size(small)))         /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (16 0.47 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft1 topright1 botleft1 botright1, xcommon scheme(plotplain)

. graph export "${main_appendix}/Figure_A1.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A1.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A2: Predicted probabilities of correctly interpreting the data (2SD)
. * The program "Clarify" is necessary to run this simulation.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. * GRAPH5: TOP-LEFT Graph
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.666, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial -2 num_con 3.332 numsq 2.776 numsq_con -5.552 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3004401     .0628546     .1936524    .4356089

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 2 num_con -3.332 numsq 2.776 numsq_con 5.552 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .546666     .0732045     .4015339    .6901401

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH5-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(6 0.40 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(6 0.60 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(medium))                                                                
>                                   ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("Low numeracy", size (medium))           
>                                                                                
>                                                           ///
>                                 name(topleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH6: TOP-RIGHT Graph
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=+1.666, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial -2 num_con -3.332 numsq 2.776 numsq_con -5.552 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .1848347     .0489881     .1031649    .2943842

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 2 num_con 3.332 numsq 2.776 numsq_con 5.552 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .561374     .0699564     .4193188    .6917983

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH6-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(8 0.28 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(6 0.58 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("High numeracy", size (medium))          
>                                                                                
>                                                           ///
>                                 name(topright2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH7: BOTTOM-LEFT Graph
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.666, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial -2 num_con 3.332 numsq 2.776 numsq_con -5.552 in
> centive 1 in_con -2 in_num -1.666 in_numsq 2.776 in_num_con 3.332 in_numsq_con 
> -5.552 if order_num_treat == 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3526428     .0495583     .2616175    .4531571

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 2 num_con -3.332 numsq 2.776 numsq_con 5.552 inc
> entive 1 in_con 2 in_num -1.666 in_numsq 2.776 in_num_con -3.332 in_numsq_con 5
> .552 if order_num_treat == 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3930101     .0510375     .2948654    .4954553

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH7-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(7 0.23 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.52 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Incentivized", orientation(vertical) si
> ze(medium))                                                                    
>                                           ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                           ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH8: BOTTOM-RIGHT Graph
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs
. * High Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.666, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial -2 num_con -3.332 numsq 2.776 numsq_con -5.552 in
> centive 1 in_con -2 in_num 1.666 in_numsq 2.776 in_num_con -3.332 in_numsq_con 
> -5.552 if order_num_treat == 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3364351     .0436773     .2524922    .4202889

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 2 num_con 3.332 numsq 2.776 numsq_con 5.552 incen
> tive 1 in_con 2 in_num 1.666 in_numsq 2.776 in_num_con 3.332 in_numsq_con 5.552
>  if order_num_treat == 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4866434     .0486354      .389971    .5782607

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH8-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(7 0.20 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.61 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                           ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botright2, replace) scheme(plotplain)

. graph close

. drop p4 p5

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft2 topright2 botleft2 botright2, xcommon scheme(plotplain)

. graph export "${main_appendix}/Figure_A2.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A2.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A21: Differences in the predicted congeniality bias
. *------------------------------------------------------------------------------
> -
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *******************************************************************************
> *
. * Model SD 1
. *******************************************************************************
> *
. * Simulation 1
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -1.666
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 1 num_con -1.666 numsq 2.776 numsq_con 2.776 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.666 1.666 numsq_con 2.77
> 6 -2.776) pr 

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5191963     .0465885     .4269628    .6112178
             Pr(correct=1) |   .4808037     .0465885     .3887822    .5730372

First Difference: congenial 1  -1 num_con -1.666 1.666 numsq_con 2.776 -2.776

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1227667     .0637956    -.2496068    .0042463

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 2
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 1.666
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 1 num_con 1.666 numsq 2.776 numsq_con 2.776 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.666 -1.666 numsq_con 2.77
> 6 -2.776) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5463108     .0438422     .4528715    .6352561
             Pr(correct=1) |   .4536892     .0438422     .3647439    .5471285

First Difference: congenial 1  -1 num_con 1.666 -1.666 numsq_con 2.776 -2.776

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1978073     .0631879    -.3195201   -.0660607

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 3
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -1.666
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.666 congenial 1 num_con -1.666 numsq 2.776 numsq_con 2.776 inc
> entive 1 in_con 1 in_num -1.666 in_numsq 2.776 in_num_con -1.666 in_numsq_con 2
> .776 if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.666 1.666 numsq_con 2.77
> 6 -2.776 in_con 1 -1 in_num_con -1.666 1.666 in_numsq_con 2.776 -2.776) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .618563     .0309631     .5567188    .6750382
             Pr(correct=1) |    .381437     .0309631     .3249618    .4432812

First Difference: congenial 1  -1 num_con -1.666 1.666 numsq_con 2.776 -2.776 in_
> con 1 -1 in_num_con -1.666 1.666 in_numsq_con 2.776 -2.776

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0201621     .0440479    -.1089315    .0652333

. drop b*

. *******************************************************************************
> ****************************************
. * Simulation 4
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 1.666
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.666 congenial 1 num_con 1.666 numsq 2.776 numsq_con 2.776 incen
> tive 1 in_con 1 in_num 1.666 in_numsq 2.776 in_num_con 1.666 in_numsq_con 2.776
>  if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.666 -1.666 numsq_con 2.77
> 6 -2.776 in_con 1 -1 in_num_con 1.666 -1.666 in_numsq_con 2.776 -2.776) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5534159     .0310528     .4939677    .6122556
             Pr(correct=1) |   .4465841     .0310528     .3877444    .5060323

First Difference: congenial 1  -1 num_con 1.666 -1.666 numsq_con 2.776 -2.776 in_
> con 1 -1 in_num_con 1.666 -1.666 in_numsq_con 2.776 -2.776

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0756817     .0417931    -.1550126     .016404

. drop b*

. *******************************************************************************
> *
. *Model SD 1.5
. *******************************************************************************
> *
. * Simulation 5
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -2.499 
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.499 congenial 1 num_con -2.499 numsq 6.245 numsq_con 6.245 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.499 2.499 numsq_con 6.24
> 5 -6.245) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4661053     .0777698     .3271023    .6208883
             Pr(correct=1) |   .5338947     .0777698     .3791117    .6728977

First Difference: congenial 1  -1 num_con -2.499 2.499 numsq_con 6.245 -6.245

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1380292     .1113026     -.353425    .0865256

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 6
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 2.499
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.499 congenial 1 num_con 2.499 numsq 6.245 numsq_con 6.245 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.499 -2.499 numsq_con 6.24
> 5 -6.245) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5063349      .060193       .38788    .6264372
             Pr(correct=1) |   .4936651      .060193     .3735628      .61212

First Difference: congenial 1  -1 num_con 2.499 -2.499 numsq_con 6.245 -6.245

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.2516904     .0888176    -.4041511   -.0648018

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 7
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -2.499
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.499 congenial 1 num_con -2.499 numsq 6.245 numsq_con 6.245 inc
> entive 1 in_con 1 in_num -2.499 in_numsq 6.245 in_num_con -2.499 in_numsq_con 6
> .245 if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.499 2.499 numsq_con 6.24
> 5 -6.245 in_con 1 -1 in_num_con -2.499 2.499 in_numsq_con 6.245 -6.245) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6096431     .0513446     .5041105    .7063293
             Pr(correct=1) |   .3903569     .0513446     .2936707    .4958895

First Difference: congenial 1  -1 num_con -2.499 2.499 numsq_con 6.245 -6.245 in_
> con 1 -1 in_num_con -2.499 2.499 in_numsq_con 6.245 -6.245

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0219124     .0743169    -.1663718    .1184521

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 8
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy= 2.499
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.499 congenial 1 num_con 2.499 numsq 6.245 numsq_con 6.245 incen
> tive 1 in_con 1 in_num 2.499 in_numsq 6.245 in_num_con 2.499 in_numsq_con 6.245
>  if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.499 -2.499 numsq_con 6.24
> 5 -6.245 in_con 1 -1 in_num_con 2.499 -2.499 in_numsq_con 6.245 -6.245) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5113213      .043567     .4235757    .5985791
             Pr(correct=1) |   .4886787      .043567     .4014209    .5764243

First Difference: congenial 1  -1 num_con 2.499 -2.499 numsq_con 6.245 -6.245 in_
> con 1 -1 in_num_con 2.499 -2.499 in_numsq_con 6.245 -6.245

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1063465     .0563397    -.2140532     .005724

. drop b*

. *******************************************************************************
> *
. *Model SD 2
. *******************************************************************************
> *
. * Simulation 9
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy= -3.332
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.332 congenial 1 num_con -3.332 numsq 11.102 numsq_con 11.102 i
> ncentive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_nu
> m_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.332 3.332 numsq_con 11.1
> 02 -11.102) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .3999872     .1218679     .1964003    .6630663
             Pr(correct=1) |   .6000128     .1218679     .3369337    .8035997

First Difference: congenial 1  -1 num_con -3.332 3.332 numsq_con 11.102 -11.102

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1611592     .1839968    -.4954446    .2081909

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 10
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy= 3.332
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.332 congenial 1 num_con 3.332 numsq 11.102 numsq_con 11.102 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.332 -3.332 numsq_con 11.1
> 02 -11.102) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4492689     .0955709     .2660893    .6307074
             Pr(correct=1) |   .5507311     .0955709     .3692926    .7339107

First Difference: congenial 1  -1 num_con 3.332 -3.332 numsq_con 11.102 -11.102

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.3146121     .1410963    -.5633442   -.0167072

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 11
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -3.332 
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.332 congenial 1 num_con -3.332 numsq 11.102 numsq_con 11.102 i
> ncentive 1 in_con 1 in_num -3.332 in_numsq 11.102 in_num_con -3.332 in_numsq_co
> n 11.102 if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.332 3.332 numsq_con 11.1
> 02 -11.102 in_con 1 -1 in_num_con -3.332 3.332 in_numsq_con 11.102 -11.102) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5900383     .0852464     .4122314    .7545024
             Pr(correct=1) |   .4099617     .0852464     .2454976    .5877686

First Difference: congenial 1  -1 num_con -3.332 3.332 numsq_con 11.102 -11.102 i
> n_con 1 -1 in_num_con -3.332 3.332 in_numsq_con 11.102 -11.102

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0293333     .1239886    -.2679469    .2150939

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 12
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 3.332
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 0, r

Iteration 0:   log pseudolikelihood = -1041.1813
Iteration 1:   log pseudolikelihood = -1028.4557
Iteration 2:   log pseudolikelihood = -1028.3946
Iteration 3:   log pseudolikelihood = -1028.3945

Logistic regression                               Number of obs   =       1558
                                                  Wald chi2(11)   =      23.96
                                                  Prob > chi2     =     0.0129
Log pseudolikelihood = -1028.3945                 Pseudo R2       =     0.0123

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0885553    .057193    -1.55   0.122    -.2006516    .0235409
   congenial |   .2864583   .1320959     2.17   0.030      .027555    .5453615
     num_con |   .0552045   .0594733     0.93   0.353    -.0613611      .17177
       numsq |   .0329447   .0318089     1.04   0.300    -.0293996     .095289
   numsq_con |    .022751   .0347975     0.65   0.513    -.0454509    .0909529
   incentive |   .0656935   .1549031     0.42   0.671     -.237911    .3692979
      in_con |  -.2094085   .1580831    -1.32   0.185    -.5192457    .1004288
      in_num |   .1337708   .0697784     1.92   0.055    -.0029924     .270534
    in_numsq |  -.0120253   .0383388    -0.31   0.754    -.0871678    .0631173
  in_num_con |  -.0204195    .071721    -0.28   0.776    -.1609901    .1201511
in_numsq_con |  -.0140364   .0409899    -0.34   0.732    -.0943752    .0663024
       _cons |  -.5758546   .1280379    -4.50   0.000    -.8268042   -.3249049
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.332 congenial 1 num_con 3.332 numsq 11.102 numsq_con 11.102 inc
> entive 1 in_con 1 in_num 3.332 in_numsq 11.102 in_num_con 3.332 in_numsq_con 11
> .102 if order_num_treat == 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.332 -3.332 numsq_con 11.1
> 02 -11.102 in_con 1 -1 in_num_con 3.332 -3.332 in_numsq_con 11.102 -11.102) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4596721     .0699387     .3228472    .6052575
             Pr(correct=1) |   .5403279     .0699387     .3947425    .6771528

First Difference: congenial 1  -1 num_con 3.332 -3.332 numsq_con 11.102 -11.102 i
> n_con 1 -1 in_num_con 3.332 -3.332 in_numsq_con 11.102 -11.102

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1421504     .0926137    -.3258055    .0373767

. drop b*

. *------------------------------------------------------------------------------
> -
. ****The results from the t-test below are used to create Table A21 manually in 
> latex.
. *------------------------------------------------------------------------------
> -
. 
. 
. *Simulation1/2 SD1 No-incentive - Low vs High Numeracy
. ttesti 1000 -.1227667 2.017394  1000 -.1978073 1.998177  

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.1227667    .0637956    2.017394   -.2479555    .0024221
       y |   1,000   -.1978073    .0631879    1.998177   -.3218035   -.0738111
---------+--------------------------------------------------------------------
Combined |   2,000    -.160287    .0448926    2.007657   -.2483281   -.0722459
---------+--------------------------------------------------------------------
    diff |            .0750406    .0897919                -.101055    .2511362
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.8357
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7983         Pr(|T| > |t|) = 0.4034          Pr(T > t) = 0.2017

. 
. *Simulation3/4 SD1 Incentive - Low vs High Numeracy
. ttesti 1000 -.0201621 1.392917  1000 -.0756817 1.321614

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0201621    .0440479    1.392917   -.1065991    .0662749
       y |   1,000   -.0756817    .0417931    1.321614    -.157694    .0063306
---------+--------------------------------------------------------------------
Combined |   2,000   -.0479219    .0303586    1.357678   -.1074597    .0116159
---------+--------------------------------------------------------------------
    diff |            .0555196    .0607197                -.063561    .1746002
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.9144
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.8197         Pr(|T| > |t|) = 0.3606          Pr(T > t) = 0.1803

. 
. *Simulation5/6 SD1.5 No-incentive - Low vs High Numeracy
. ttesti 1000 -.1380292 3.519697  1000 -.2516904 2.808659

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.1380292    .1113026    3.519697   -.3564429    .0803845
       y |   1,000   -.2516904    .0888176    2.808659   -.4259809   -.0773999
---------+--------------------------------------------------------------------
Combined |   2,000   -.1948598    .0711919    3.183799   -.3344779   -.0552417
---------+--------------------------------------------------------------------
    diff |            .1136612    .1423967               -.1656005    .3929229
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.7982
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7876         Pr(|T| > |t|) = 0.4248          Pr(T > t) = 0.2124

. 
. *Simulation7/8 SD1.5 Incentive - Low vs High Numeracy
. ttesti 1000 -.0219124 2.350107  1000 -.1063465 1.781618

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0219124    .0743169    2.350107   -.1677476    .1239228
       y |   1,000   -.1063465    .0563397    1.781618   -.2169042    .0042112
---------+--------------------------------------------------------------------
Combined |   2,000   -.0641294    .0466272    2.085232   -.1555724    .0273135
---------+--------------------------------------------------------------------
    diff |            .0844341    .0932586               -.0984602    .2673284
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.9054
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.8173         Pr(|T| > |t|) = 0.3654          Pr(T > t) = 0.1827

. 
. *Simulation9/10 SD2 No-incentive - Low vs High Numeracy
. ttesti 1000 -.1611592 5.818490  1000 -.3146121 4.461857

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.1611592    .1839968     5.81849   -.5222238    .1999054
       y |   1,000   -.3146121    .1410963    4.461857   -.5914912    -.037733
---------+--------------------------------------------------------------------
Combined |   2,000   -.2378857    .1159179    5.184008   -.4652183    -.010553
---------+--------------------------------------------------------------------
    diff |            .1534529    .2318685               -.3012764    .6081822
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.6618
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7459         Pr(|T| > |t|) = 0.5082          Pr(T > t) = 0.2541

. 
. *Simulation11/12 SD2 Incentive - Low vs High Numeracy
. ttesti 1000 -.0293333 3.920864  1000 -.1421504 2.928702

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0293333    .1239886    3.920864   -.2726413    .2139747
       y |   1,000   -.1421504    .0926137    2.928702   -.3238901    .0395893
---------+--------------------------------------------------------------------
Combined |   2,000   -.0857419    .0773706     3.46012   -.2374774    .0659937
---------+--------------------------------------------------------------------
    diff |            .1128171    .1547594               -.1906896    .4163238
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.7290
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7670         Pr(|T| > |t|) = 0.4661          Pr(T > t) = 0.2330

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Split sample analyses - Numeracy *BEFORE* treatment
. * Table A22: The impact of numeracy and congeniality on accuracy
. * Table A23: The impatc of incentive, numeracy, and congeniality on accuracy
. * Figure A3: Predicted probabilities of correctly interpreting the data (-1,0,1
> SD)
. * Figure A4: Predicted probabilities of correctly interpreting the data (2SD)
. * Table A24: Differences in the predicted congeneity bias
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A22: The impact of numeracy and congeniality on accuracy
. *------------------------------------------------------------------------------
> -
. * Numeracy is measured before (order_num_treat == 1)
. * Equation 1 (without control variables) - Table A22 (1)
. reg correct congenial numeracy numsq if incentive==0 & order_num_treat==1, r

Linear regression                               Number of obs     =        497
                                                F(3, 493)         =       0.33
                                                Prob > F          =     0.8039
                                                R-squared         =     0.0020
                                                Root MSE          =     .49997

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0167781   .0226304     0.74   0.459    -.0276857     .061242
    numeracy |   .0099774    .014001     0.71   0.476    -.0175317    .0374865
       numsq |  -.0006527   .0077765    -0.08   0.933    -.0159319    .0146265
       _cons |   .4630071   .0307845    15.04   0.000      .402522    .5234922
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A22 (2)
. reg correct congenial numeracy numsq age i.gender i.race i.edu i.vote2016 if in
> centive==0 & order_num_treat==1, r

Linear regression                               Number of obs     =        497
                                                F(21, 474)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.0538
                                                Root MSE          =     .49649

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0196741   .0230618     0.85   0.394    -.0256419      .06499
      numeracy |   .0035314   .0154266     0.23   0.819    -.0267815    .0338443
         numsq |  -.0008869   .0080209    -0.11   0.912    -.0166479    .0148741
           age |    .001445   .0015055     0.96   0.338    -.0015133    .0044032
               |
        gender |
         Male  |    .075679   .0476277     1.59   0.113    -.0179085    .1692666
        Other  |   .0721557   .2990166     0.24   0.809    -.5154062    .6597177
               |
          race |
Non-hispani..  |   .1366007   .1018135     1.34   0.180     -.063461    .3366624
     Hispanic  |   .0340739   .0657781     0.52   0.605    -.0951788    .1633265
        Asian  |   .3287982   .1031511     3.19   0.002     .1261083    .5314881
American In..  |  -.3923613   .0820529    -4.78   0.000    -.5535938   -.2311289
       Others  |  -.0379306   .1337636    -0.28   0.777    -.3007736    .2249123
Prefer not ..  |   -.199823    .253631    -0.79   0.431    -.6982032    .2985572
               |
           edu |
High school..  |   .0428792   .1090357     0.39   0.694    -.1713739    .2571324
 Some college  |  -.0063266   .1132837    -0.06   0.955     -.228927    .2162739
 College grad  |  -.0744158   .1177301    -0.63   0.528    -.3057533    .1569217
    Post grad  |   .0744369   .1224074     0.61   0.543    -.1660913     .314965
        Other  |   .0799936   .3529257     0.23   0.821    -.6134987     .773486
               |
      vote2016 |
      Clinton  |  -.0042956   .0608317    -0.07   0.944    -.1238287    .1152376
Other candi..  |   .1716184    .107321     1.60   0.110    -.0392655    .3825022
      No vote  |   -.026779   .0675125    -0.40   0.692    -.1594398    .1058818
      Not say  |   .0890914   .1331979     0.67   0.504    -.1726401    .3508228
        Other  |  -.3869582    .065411    -5.92   0.000    -.5154896   -.2584268
               |
         _cons |   .3255561    .147483     2.21   0.028     .0357547    .6153575
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Equation 2 (without control variables) - Table A22 (3)
. reg correct congenial numeracy numsq num_con c.numsq#c.congenial  if incentive=
> =0 & order_num_treat==1, r

Linear regression                               Number of obs     =        497
                                                F(5, 491)         =       1.08
                                                Prob > F          =     0.3680
                                                R-squared         =     0.0104
                                                Root MSE          =     .49889

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0484316   .0312442     1.55   0.122    -.0129573    .1098205
    numeracy |   .0067112   .0140957     0.48   0.634    -.0209842    .0344066
       numsq |   .0010506   .0078104     0.13   0.893    -.0142953    .0163966
     num_con |    .025032   .0140538     1.78   0.076     -.002581    .0526449
             |
     c.numsq#|
 c.congenial |  -.0120849   .0077927    -1.55   0.122    -.0273961    .0032263
             |
       _cons |   .4622305   .0307317    15.04   0.000     .4018487    .5226123
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table A22 (4)
. reg correct congenial numeracy numsq num_con c.numsq#c.congenial age i.gender i
> .race i.edu i.vote2016 if incentive==0 & order_num_treat==1, r

Linear regression                               Number of obs     =        497
                                                F(23, 472)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.0603
                                                Root MSE          =     .49583

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0528867   .0314651     1.68   0.093    -.0089424    .1147157
      numeracy |   .0000556   .0154665     0.00   0.997    -.0303361    .0304473
         numsq |   .0007275   .0080246     0.09   0.928     -.015041    .0164959
       num_con |   .0197292    .014821     1.33   0.184    -.0093941    .0488525
               |
       c.numsq#|
   c.congenial |  -.0124585   .0079946    -1.56   0.120    -.0281679     .003251
               |
           age |   .0016137   .0015132     1.07   0.287    -.0013597    .0045872
               |
        gender |
         Male  |   .0725966   .0477087     1.52   0.129    -.0211512    .1663444
        Other  |   .0747663   .2884639     0.26   0.796    -.4920661    .6415987
               |
          race |
Non-hispani..  |   .1333526   .1011408     1.32   0.188    -.0653893    .3320945
     Hispanic  |   .0284472   .0660928     0.43   0.667    -.1014254    .1583198
        Asian  |   .3207039   .1026465     3.12   0.002     .1190033    .5224045
American In..  |  -.4240994   .0908292    -4.67   0.000     -.602579   -.2456197
       Others  |  -.0365332   .1319868    -0.28   0.782    -.2958876    .2228212
Prefer not ..  |  -.1667391   .2655031    -0.63   0.530    -.6884534    .3549752
               |
           edu |
High school..  |   .0404775   .1105004     0.37   0.714    -.1766561    .2576111
 Some college  |  -.0075203   .1145951    -0.07   0.948    -.2326998    .2176593
 College grad  |  -.0700913   .1185732    -0.59   0.555    -.3030879    .1629054
    Post grad  |   .0741862   .1236582     0.60   0.549    -.1688026    .3171749
        Other  |   .0433316   .3789403     0.11   0.909    -.7012872    .7879503
               |
      vote2016 |
      Clinton  |  -.0113277   .0608457    -0.19   0.852    -.1308896    .1082343
Other candi..  |   .1582814    .106265     1.49   0.137    -.0505295    .3670923
      No vote  |  -.0327544    .067516    -0.49   0.628    -.1654235    .0999146
      Not say  |   .0820865   .1343635     0.61   0.542    -.1819382    .3461111
        Other  |  -.3860039   .0679019    -5.68   0.000    -.5194312   -.2525766
               |
         _cons |   .3236325   .1485614     2.18   0.030      .031709    .6155559
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Export Table A22 in Latex
. esttab  a1 a2 a3 a4 using "${main_appendix}/Table_A22.tex" ,  ///
>                 nonumbers mtitles("(1)" "(2)" "(3)" "(4)") b(3) star(* 0.10 ** 
> 0.05  *** 0.01) se(3) ar2  label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A22.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A23: The impact of incentive, numeracy, and congeniality on accuracy
. *------------------------------------------------------------------------------
> -
. * Numeracy is measured before (order_num_treat == 1)
. * Equation 3 (without control variables) - Table A23 (5)
. reg correct incentive if order_num_treat==1, r

Linear regression                               Number of obs     =      1,492
                                                F(1, 1490)        =       0.04
                                                Prob > F          =     0.8412
                                                R-squared         =     0.0000
                                                Root MSE          =     .49848

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |  -.0054882   .0273893    -0.20   0.841    -.0592138    .0482374
       _cons |   .4607646   .0223739    20.59   0.000     .4168769    .5046523
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A23 (6)
. reg correct incentive age i.gender i.race i.edu i.vote2016 if order_num_treat==
> 1, r

Linear regression                               Number of obs     =      1,492
                                                F(21, 1470)       =      12.47
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0152
                                                Root MSE          =     .49805

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |  -.0084988    .027586    -0.31   0.758    -.0626109    .0456133
           age |  -.0000567   .0008656    -0.07   0.948    -.0017546    .0016412
               |
        gender |
         Male  |   .0373636   .0268905     1.39   0.165    -.0153842    .0901114
        Other  |   .0641859   .2372475     0.27   0.787     -.401194    .5295657
      Not say  |   .5177187   .0790296     6.55   0.000      .362696    .6727414
               |
          race |
Non-hispani..  |  -.0062231   .0596565    -0.10   0.917     -.123244    .1107978
     Hispanic  |   .0188257   .0394256     0.48   0.633    -.0585106    .0961621
        Asian  |   .0742208    .060669     1.22   0.221    -.0447862    .1932278
American In..  |  -.0398653   .2091316    -0.19   0.849    -.4500935    .3703629
       Others  |  -.0010379   .0842783    -0.01   0.990    -.1663565    .1642806
Prefer not ..  |   .0074433   .1154163     0.06   0.949     -.218955    .2338415
               |
           edu |
High school..  |   .0142431   .0735601     0.19   0.846    -.1300508    .1585371
 Some college  |   -.031811   .0752834    -0.42   0.673    -.1794853    .1158634
 College grad  |  -.0626718   .0763344    -0.82   0.412    -.2124078    .0870643
    Post grad  |   .0548237   .0796712     0.69   0.491    -.1014577    .2111052
        Other  |  -.0175487   .1690794    -0.10   0.917    -.3492113    .3141138
               |
      vote2016 |
      Clinton  |   .0130941   .0331369     0.40   0.693    -.0519064    .0780947
Other candi..  |   .0589436    .064122     0.92   0.358    -.0668367    .1847239
      No vote  |  -.0531348   .0378991    -1.40   0.161    -.1274768    .0212072
      Not say  |   .0087165    .080488     0.11   0.914     -.149167    .1666001
        Other  |   .0907497   .1795415     0.51   0.613    -.2614351    .4429345
               |
         _cons |   .4597569   .0927405     4.96   0.000      .277839    .6416748
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Equation 4 (excl. 2 variables) (without control variables) - Table A23 (7)
. reg correct numeracy congenial num_con numsq c.numsq#c.congenial incentive in_c
> on in_num in_num_con if order_num_treat==1, r

Linear regression                               Number of obs     =      1,492
                                                F(9, 1482)        =       2.14
                                                Prob > F          =     0.0237
                                                R-squared         =     0.0125
                                                Root MSE          =     .49669

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0072334   .0138112     0.52   0.601    -.0198581    .0343249
   congenial |   .0251736   .0258806     0.97   0.331    -.0255928    .0759401
     num_con |   .0206638   .0136676     1.51   0.131    -.0061461    .0474738
       numsq |   .0028649   .0045249     0.63   0.527     -.006011    .0117408
             |
     c.numsq#|
 c.congenial |  -.0037455   .0046594    -0.80   0.422    -.0128853    .0053942
             |
   incentive |  -.0075959   .0273762    -0.28   0.781    -.0612962    .0461043
      in_con |   .0018068   .0275899     0.07   0.948    -.0523126    .0559262
      in_num |   .0149617   .0167968     0.89   0.373    -.0179863    .0479098
  in_num_con |   .0064034   .0165993     0.39   0.700    -.0261572    .0389641
       _cons |   .4559304   .0254882    17.89   0.000     .4059336    .5059272
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a7

. 
. * Equation 4 (excl. 2 variables) (with control variables) - Table A23 (8)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_num_con age i.gender i.race i.edu i.vote2016 if order_num_treat==
> 1, r

Linear regression                               Number of obs     =      1,492
                                                F(29, 1462)       =      10.37
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0261
                                                Root MSE          =     .49662

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0253095     .02599     0.97   0.330    -.0256721    .0762911
      numeracy |   .0058691   .0142002     0.41   0.679    -.0219857     .033724
       num_con |   .0188544    .013801     1.37   0.172    -.0082175    .0459263
         numsq |   .0032444   .0045715     0.71   0.478    -.0057231    .0122118
               |
       c.numsq#|
   c.congenial |  -.0040216   .0046991    -0.86   0.392    -.0132393     .005196
               |
     incentive |   -.009318   .0276172    -0.34   0.736    -.0634916    .0448555
        in_con |   .0028988      .0278     0.10   0.917    -.0516333    .0574309
        in_num |   .0142587   .0168025     0.85   0.396    -.0187009    .0472184
    in_num_con |   .0079982   .0167636     0.48   0.633    -.0248851    .0408816
           age |  -8.05e-06   .0008639    -0.01   0.993    -.0017027    .0016866
               |
        gender |
         Male  |    .025889   .0272126     0.95   0.342     -.027491     .079269
        Other  |   .0688617    .226701     0.30   0.761    -.3758322    .5135557
      Not say  |   .5320268   .0790646     6.73   0.000     .3769345     .687119
               |
          race |
Non-hispani..  |   .0022935   .0611654     0.04   0.970    -.1176879    .1222749
     Hispanic  |   .0194555   .0396211     0.49   0.623    -.0582647    .0971757
        Asian  |   .0601188   .0608351     0.99   0.323    -.0592147    .1794523
American In..  |  -.0853876   .2104798    -0.41   0.685    -.4982621     .327487
       Others  |   .0155032   .0847114     0.18   0.855    -.1506656    .1816721
Prefer not ..  |   .0246575   .1175089     0.21   0.834    -.2058464    .2551615
               |
           edu |
High school..  |   .0081897   .0740537     0.11   0.912    -.1370732    .1534525
 Some college  |  -.0489247    .075986    -0.64   0.520     -.197978    .1001286
 College grad  |   -.078675   .0775609    -1.01   0.311    -.2308176    .0734676
    Post grad  |   .0309381   .0808886     0.38   0.702    -.1277321    .1896083
        Other  |   -.022475   .1658706    -0.14   0.892    -.3478447    .3028948
               |
      vote2016 |
      Clinton  |   .0041132   .0331701     0.12   0.901    -.0609529    .0691793
Other candi..  |   .0429706   .0654962     0.66   0.512     -.085506    .1714472
      No vote  |  -.0612107   .0379071    -1.61   0.107    -.1355688    .0131473
      Not say  |   .0006409   .0813799     0.01   0.994     -.158993    .1602748
        Other  |   .0955763   .1749874     0.55   0.585    -.2476768    .4388295
               |
         _cons |   .4757036   .0953954     4.99   0.000     .2885772      .66283
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a8

. 
. * Equation 4 (without control variables) - Table A23 (9)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con if order_num_treat==1, r

Linear regression                               Number of obs     =      1,492
                                                F(11, 1480)       =       1.93
                                                Prob > F          =     0.0320
                                                R-squared         =     0.0138
                                                Root MSE          =     .49672

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0484316   .0311807     1.55   0.121    -.0127315    .1095947
    numeracy |   .0067112   .0140671     0.48   0.633    -.0208823    .0343047
     num_con |    .025032   .0140252     1.78   0.075    -.0024794    .0525434
       numsq |   .0010506   .0077945     0.13   0.893    -.0142389    .0163401
             |
     c.numsq#|
 c.congenial |  -.0120849   .0077769    -1.55   0.120    -.0273398      .00317
             |
   incentive |  -.0169954   .0375271    -0.45   0.651    -.0906072    .0566165
      in_con |  -.0335287   .0384673    -0.87   0.384    -.1089848    .0419275
      in_num |   .0147706   .0173463     0.85   0.395    -.0192554    .0487966
    in_numsq |   .0026372   .0095677     0.28   0.783    -.0161305     .021405
  in_num_con |  -.0007289   .0173984    -0.04   0.967    -.0348571    .0333993
in_numsq_con |   .0126225   .0096911     1.30   0.193    -.0063872    .0316322
       _cons |   .4622305   .0306692    15.07   0.000     .4020708    .5223902
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a9

. 
. * Equation 4 (without control variables) - Table A23 (10)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con age i.gender i.race i.edu i.vote201
> 6 if order_num_treat==1, r

Linear regression                               Number of obs     =      1,492
                                                F(31, 1460)       =       9.70
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0273
                                                Root MSE          =     .49667

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0479507   .0311568     1.54   0.124    -.0131661    .1090676
      numeracy |   .0051939   .0144471     0.36   0.719    -.0231453    .0335332
       num_con |   .0231812   .0141741     1.64   0.102    -.0046225    .0509849
         numsq |   .0018929   .0077661     0.24   0.807     -.013341    .0171268
               |
       c.numsq#|
   c.congenial |  -.0121357   .0077465    -1.57   0.117    -.0273311    .0030597
               |
     incentive |  -.0168332   .0376979    -0.45   0.655     -.090781    .0571147
        in_con |  -.0313482   .0385098    -0.81   0.416    -.1068886    .0441922
        in_num |   .0143821   .0173536     0.83   0.407    -.0196586    .0484227
      in_numsq |   .0019414   .0095574     0.20   0.839    -.0168062     .020689
    in_num_con |   .0010066   .0175537     0.06   0.954    -.0334266    .0354397
  in_numsq_con |    .012273   .0097006     1.27   0.206    -.0067557    .0313017
           age |   .0000299   .0008653     0.03   0.972    -.0016675    .0017273
               |
        gender |
         Male  |   .0245882   .0272501     0.90   0.367    -.0288654    .0780418
        Other  |   .0734738   .2274165     0.32   0.747    -.3726241    .5195717
      Not say  |   .5316052   .0793708     6.70   0.000     .3759122    .6872982
               |
          race |
Non-hispani..  |   .0044802   .0607634     0.07   0.941    -.1147127    .1236731
     Hispanic  |   .0181237   .0397002     0.46   0.648    -.0597518    .0959992
        Asian  |   .0611836   .0610723     1.00   0.317    -.0586152    .1809823
American In..  |  -.0982083   .2165462    -0.45   0.650    -.5229832    .3265667
       Others  |   .0139264   .0841949     0.17   0.869    -.1512296    .1790823
Prefer not ..  |   .0271437   .1179641     0.23   0.818    -.2042535    .2585409
               |
           edu |
High school..  |   .0073618   .0742439     0.10   0.921    -.1382744     .152998
 Some college  |  -.0491405   .0761849    -0.65   0.519    -.1985841    .1003031
 College grad  |  -.0779383    .077716    -1.00   0.316    -.2303852    .0745085
    Post grad  |   .0310515   .0810461     0.38   0.702    -.1279278    .1900307
        Other  |  -.0240521   .1672628    -0.14   0.886    -.3521532    .3040489
               |
      vote2016 |
      Clinton  |   .0040471   .0332252     0.12   0.903    -.0611272    .0692213
Other candi..  |   .0444051   .0652099     0.68   0.496      -.08351    .1723201
      No vote  |  -.0600062   .0379269    -1.58   0.114    -.1344032    .0143907
      Not say  |    .000012   .0814944     0.00   1.000    -.1598466    .1598706
        Other  |    .102939    .174914     0.59   0.556    -.2401705    .4460484
               |
         _cons |   .4791758   .0968569     4.95   0.000     .2891823    .6691693
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a10

. 
. * Export Table A23 in Latex
. esttab  a5 a6 a7 a8 a9 a10 using "${main_appendix}/Table_A23.tex" ,  ///
>                 nonumbers mtitles("(5)" "(6)" "(7)" "(8)" "(9)" "(10)") b(3) st
> ar(* 0.10 ** 0.05  *** 0.01) se(3) ar2 label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")                                     
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A23.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A3: Predicted probabilities of correctly interpreting the data (-1,0,1
> SD)
. *------------------------------------------------------------------------------
> -
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. * GRAPH1: TOP-LEFT Graph (Non-incentivized & Low numeracy)
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.641, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial -1 num_con 1.641 numsq 2.693 numsq_con -2.693 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 1

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .481247     .0497182     .3840541    .5778687

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 1 num_con -1.641 numsq 2.693 numsq_con 2.693 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4262502      .043175     .3439383     .517069

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 0 num_con 0 numsq 2.693 numsq_con 0 incentive 0 
> in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_treat == 
> 1

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4541101     .0319989     .3920376    .5159531

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000     .481247    .0497182   .3011599   .6263377
          p2 |      1,000    .4262502     .043175   .2894824   .5771186
          p3 |      1,000    .4541101    .0319989   .3422084   .5506288

. *-------------------------------------------------------GRAPH1-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(8 0.56 "Cong
> enial = -1", color (orange) size(small)))        ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(8 0.33 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (12 0.53 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%" 0.7 "70%")                                                           
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("Low numeracy", size (medium))           
>                                                                                
>                                                   ///
>                                 name(topleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH2: TOP-RIGHT Graph (Non-incentivized & High numeracy)
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=+1.641, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial -1 num_con -1.641 numsq 2.693 numsq_con -2.693 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 1

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4167502     .0441244     .3285657     .511276

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 1 num_con 1.641 numsq 2.693 numsq_con 2.693 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 1

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .5356042     .0442604     .4491112    .6256652

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 0 num_con 0 numsq 2.693 numsq_con 0 incentive 0 i
> n_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_treat == 1

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4759563     .0319469      .416263    .5409451

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4167502    .0441244   .3007587   .5563308
          p2 |      1,000    .5356042    .0442604   .3920072   .6728337
          p3 |      1,000    .4759563    .0319469    .387595   .5835662

. *-------------------------------------------------------GRAPH2-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(8 0.33 "Cong
> enial = -1", color (orange) size(small)))        ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9.5 0.57 "Congenial = +1", color (green) size(small)))        /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (11 0.41 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%" 0.7 "70%")                                                           
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("High numeracy", size (medium))          
>                                                                                
>                                                   ///
>                                 name(topright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH3: BOTTOM-LEFT Graph (Incentivized & Low numeracy)
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.641, incentive =1
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial -1 num_con 1.641 numsq 2.693 numsq_con -2.693 in
> centive 1 in_con -1 in_num -1.641 in_numsq 2.693 in_num_con 1.641 in_numsq_con 
> -2.693 if order_num_treat == 1

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4445688     .0327395     .3814811    .5099578

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 1 num_con -1.641 numsq 2.693 numsq_con 2.693 inc
> entive 1 in_con 1 in_num -1.641 in_numsq 2.693 in_num_con -1.641 in_numsq_con 2
> .693 if order_num_treat == 1

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3959303     .0315977     .3368291    .4596373

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 0 num_con 0 numsq 2.693 numsq_con 0 incentive 1 
> in_con 0 in_num -1.641 in_numsq 2.693 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4196873     .0219181     .3788681     .462582

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4445688    .0327395   .3430342     .54941
          p2 |      1,000    .3959303    .0315977   .2828908   .5026581
          p3 |      1,000    .4196873    .0219181   .3341584    .506136

. *-------------------------------------------------------GRAPH3-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(11 0.52 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.30 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (15 0.50 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("  Incentivized  ", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%" 0.7 "70%")                                                           
>                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH4: BOTTOM-RIGHT Graph (Incentivized & High numeracy)
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs.*/
. * High Numeracy, Incentive=1*/
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=1.641, incentive =1*/
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial -1 num_con -1.641 numsq 2.693 numsq_con -2.693 in
> centive 1 in_con -1 in_num 1.641 in_numsq 2.693 in_num_con -1.641 in_numsq_con 
> -2.693 if order_num_treat == 1

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4335616     .0335478     .3670833    .5011685

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 1 num_con 1.641 numsq 2.693 numsq_con 2.693 incen
> tive 1 in_con 1 in_num 1.641 in_numsq 2.693 in_num_con 1.641 in_numsq_con 2.693
>  if order_num_treat == 1

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .5491599      .033243     .4838029    .6142701

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 0 num_con 0 numsq 2.693 numsq_con 0 incentive 1 i
> n_con 0 in_num 1.641 in_numsq 2.693 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 1

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4910872     .0234624     .4450264    .5350097

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4335616    .0335478   .3436495   .5426585
          p2 |      1,000    .5491599     .033243    .445045   .6434118
          p3 |      1,000    .4910872    .0234624   .4241074   .5554491

. *-------------------------------------------------------GRAPH4-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.35 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(13 0.58 "Congenial = +1", color (green) size(small)))         /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (15 0.42 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%" 0.7 "70%")                                                           
>                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft1 topright1 botleft1 botright1, xcommon scheme(plotplain)

. graph export "${main_appendix}/Figure_A3.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A3.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A4: Predicted probabilities of correctly interpreting the data (2SD)
. *------------------------------------------------------------------------------
> -
. * GRAPH5: TOP-LEFT Graph
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.641, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial -2 num_con 3.282 numsq 2.693 numsq_con -5.386 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 1

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .5032851     .0785415     .3543542    .6589779

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 2 num_con -3.282 numsq 2.693 numsq_con 5.386 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4065051     .0685163     .2798633    .5472585

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH5-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(5.3 0.57 "Co
> ngenial = -2", color (dknavy) size(small)))              ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(5 0.26 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(medium))                                                                
>                                   ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("Low numeracy", size (medium))           
>                                                                                
>                                                           ///
>                                 name(topleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH6: TOP-RIGHT Graph
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=+1.641, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial -2 num_con -3.282 numsq 2.693 numsq_con -5.386 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num
> _treat == 1

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3655158     .0656988     .2430809    .5001834

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 2 num_con 3.282 numsq 2.693 numsq_con 5.386 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 1

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .5893704      .069947      .444925    .7181295

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH6-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(5 0.23 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(5.2 0.48 "Congenial = +2", color (dkorange) size(small)))  /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("High numeracy", size (medium))          
>                                                                                
>                                                           ///
>                                 name(topright2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH7: BOTTOM-LEFT Graph
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.641, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial -2 num_con 3.282 numsq 2.693 numsq_con -5.386 in
> centive 1 in_con -2 in_num -1.641 in_numsq 2.693 in_num_con 3.282 in_numsq_con 
> -5.386 if order_num_treat == 1

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4679737     .0550535     .3623155    .5766224

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 2 num_con -3.282 numsq 2.693 numsq_con 5.386 inc
> entive 1 in_con 2 in_num -1.641 in_numsq 2.693 in_num_con -3.282 in_numsq_con 5
> .386 if order_num_treat == 1

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3745374     .0495882      .280663    .4719497

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH7-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(7 0.58 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.25 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Incentivized", orientation(vertical) si
> ze(medium))                                                                    
>                                           ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                           ///                                  
>                                                            ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH8: BOTTOM-RIGHT Graph
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs
. * High Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.641, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial -2 num_con -3.282 numsq 2.693 numsq_con -5.386 in
> centive 1 in_con -2 in_num 1.641 in_numsq 2.693 in_num_con -3.282 in_numsq_con 
> -5.386 if order_num_treat == 1

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3815223      .049926     .2856972    .4769062

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 2 num_con 3.282 numsq 2.693 numsq_con 5.386 incen
> tive 1 in_con 2 in_num 1.641 in_numsq 2.693 in_num_con 3.282 in_numsq_con 5.386
>  if order_num_treat == 1

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .6051523     .0511214     .4989576    .6993594

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH8-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(6 0.24 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.50 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%" 0.8 "80%")                                       
>           ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                           ///                                  
>                                                            ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botright2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft2 topright2 botleft2 botright2, xcommon scheme(plotplain)

. graph export "${main_appendix}/Figure_A4.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A4.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A24: Differences in the predicted congeniality bias
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. 
. *******************************************************************************
> *
. * Model SD 1
. *******************************************************************************
> *
. * Simulation 1
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -1.641
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 1 num_con -1.641 numsq 2.693 numsq_con 2.693 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.641 1.641 numsq_con 2.69
> 3 -2.693) pr 

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5718447     .0429841     .4854189    .6558416
             Pr(correct=1) |   .4281553     .0429841     .3441584    .5145811

First Difference: congenial 1  -1 num_con -1.641 1.641 numsq_con 2.693 -2.693

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0536047     .0665304    -.0814212     .190643

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 2
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 1.641
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 1 num_con 1.641 numsq 2.693 numsq_con 2.693 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.641 -1.641 numsq_con 2.69
> 3 -2.693) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .465532     .0459641     .3700755    .5601527
             Pr(correct=1) |    .534468     .0459641     .4398473    .6299245

First Difference: congenial 1  -1 num_con 1.641 -1.641 numsq_con 2.693 -2.693

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1161485     .0668651    -.2437636     .019991

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 3
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -1.641
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.641 congenial 1 num_con -1.641 numsq 2.693 numsq_con 2.693 inc
> entive 1 in_con 1 in_num -1.641 in_numsq 2.693 in_num_con -1.641 in_numsq_con 2
> .693 if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.641 1.641 numsq_con 2.69
> 3 -2.693 in_con 1 -1 in_num_con -1.641 1.641 in_numsq_con 2.693 -2.693) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6038291     .0309624     .5409719    .6602784
             Pr(correct=1) |   .3961709     .0309624     .3397216    .4590281

First Difference: congenial 1  -1 num_con -1.641 1.641 numsq_con 2.693 -2.693 in_
> con 1 -1 in_num_con -1.641 1.641 in_numsq_con 2.693 -2.693

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0471925     .0463069    -.0486443    .1361674

. drop b*

. *******************************************************************************
> ****************************************
. * Simulation 4
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 1.641
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.641 congenial 1 num_con 1.641 numsq 2.693 numsq_con 2.693 incen
> tive 1 in_con 1 in_num 1.641 in_numsq 2.693 in_num_con 1.641 in_numsq_con 2.693
>  if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.641 -1.641 numsq_con 2.69
> 3 -2.693 in_con 1 -1 in_num_con 1.641 -1.641 in_numsq_con 2.693 -2.693) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4510808     .0333792     .3873682    .5153654
             Pr(correct=1) |   .5489192     .0333792     .4846346    .6126318

First Difference: congenial 1  -1 num_con 1.641 -1.641 numsq_con 2.693 -2.693 in_
> con 1 -1 in_num_con 1.641 -1.641 in_numsq_con 2.693 -2.693

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1137994     .0469307    -.2023975   -.0143584

. drop b*

. *******************************************************************************
> *
. *Model SD 1.5
. *******************************************************************************
> *
. * Simulation 5
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -2.462
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.462 congenial 1 num_con -2.462 numsq 6.061 numsq_con 6.061 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.462 2.462 numsq_con 6.06
> 1 -6.061) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6337548      .064425     .5114712    .7563055
             Pr(correct=1) |   .3662452      .064425     .2436945    .4885288

First Difference: congenial 1  -1 num_con -2.462 2.462 numsq_con 6.061 -6.061

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .1755068     .1102842    -.0413211    .3998201

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 6
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 2.462
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.462 congenial 1 num_con 2.462 numsq 6.061 numsq_con 6.061 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_tr
> eat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.462 -2.462 numsq_con 6.06
> 1 -6.061) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .478517     .0632462     .3562964    .6087716
             Pr(correct=1) |    .521483     .0632462     .3912284    .6437036

First Difference: congenial 1  -1 num_con 2.462 -2.462 numsq_con 6.061 -6.061

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0745441      .087107    -.2336149    .1034218

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 7
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -2.462
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.462 congenial 1 num_con -2.462 numsq 6.061 numsq_con 6.061 inc
> entive 1 in_con 1 in_num -2.462 in_numsq 6.061 in_num_con -2.462 in_numsq_con 6
> .061 if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.462 2.462 numsq_con 6.06
> 1 -6.061 in_con 1 -1 in_num_con -2.462 2.462 in_numsq_con 6.061 -6.061) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6253545     .0515928     .5172827    .7228847
             Pr(correct=1) |   .3746455     .0515928     .2771153    .4827173

First Difference: congenial 1  -1 num_con -2.462 2.462 numsq_con 6.061 -6.061 in_
> con 1 -1 in_num_con -2.462 2.462 in_numsq_con 6.061 -6.061

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |    .080015     .0796249    -.0785249     .232913

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 8
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy= 2.462
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.462 congenial 1 num_con 2.462 numsq 6.061 numsq_con 6.061 incen
> tive 1 in_con 1 in_num 2.462 in_numsq 6.061 in_num_con 2.462 in_numsq_con 6.061
>  if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.462 -2.462 numsq_con 6.06
> 1 -6.061 in_con 1 -1 in_num_con 2.462 -2.462 in_numsq_con 6.061 -6.061) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .3991262     .0430223     .3165768    .4868276
             Pr(correct=1) |   .6008738     .0430223     .5131724    .6834232

First Difference: congenial 1  -1 num_con 2.462 -2.462 numsq_con 6.061 -6.061 in_
> con 1 -1 in_num_con 2.462 -2.462 in_numsq_con 6.061 -6.061

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1588158     .0632841    -.2812654    -.029687

. drop b*

. *******************************************************************************
> *
. *Model SD 2
. *******************************************************************************
> *
. * Simulation 9
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy= -3.282
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.282 congenial 1 num_con -3.282 numsq 10.772 numsq_con 10.772 i
> ncentive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_nu
> m_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.282 3.282 numsq_con 10.7
> 72 -10.772) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .699795     .0945688     .4989613    .8689446
             Pr(correct=1) |    .300205     .0945688     .1310554    .5010387

First Difference: congenial 1  -1 num_con -3.282 3.282 numsq_con 10.772 -10.772

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .3118046     .1680707    -.0283308    .6220541

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 10
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy= 3.282
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.282 congenial 1 num_con 3.282 numsq 10.772 numsq_con 10.772 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0 if order_num_
> treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.282 -3.282 numsq_con 10.7
> 72 -10.772) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5068022     .0990945     .3088297    .6928112
             Pr(correct=1) |   .4931978     .0990945     .3071888    .6911703

First Difference: congenial 1  -1 num_con 3.282 -3.282 numsq_con 10.772 -10.772

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0001605     .1364784    -.2687356     .273722

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 11
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -3.282
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.282 congenial 1 num_con -3.282 numsq 10.772 numsq_con 10.772 i
> ncentive 1 in_con 1 in_num -3.282 in_numsq 10.772 in_num_con -3.282 in_numsq_co
> n 10.772 if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.282 3.282 numsq_con 10.7
> 72 -10.772 in_con 1 -1 in_num_con -3.282 3.282 in_numsq_con 10.772 -10.772) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6388753      .084748     .4546153    .7953818
             Pr(correct=1) |   .3611247      .084748     .2046182    .5453847

First Difference: congenial 1  -1 num_con -3.282 3.282 numsq_con 10.772 -10.772 i
> n_con 1 -1 in_num_con -3.282 3.282 in_numsq_con 10.772 -10.772

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |    .108679     .1329356     -.154391    .3624944

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 12
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 3.282
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con if order_num_treat == 1, r

Iteration 0:   log pseudolikelihood = -1028.6782
Iteration 1:   log pseudolikelihood = -1018.3359
Iteration 2:   log pseudolikelihood = -1018.3307
Iteration 3:   log pseudolikelihood = -1018.3307

Logistic regression                               Number of obs   =       1492
                                                  Wald chi2(11)   =      19.28
                                                  Prob > chi2     =     0.0562
Log pseudolikelihood = -1018.3307                 Pseudo R2       =     0.0101

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |   .0277059   .0571867     0.48   0.628     -.084378    .1397898
   congenial |   .1975736   .1278259     1.55   0.122    -.0529606    .4481078
     num_con |   .1031177   .0588095     1.75   0.080    -.0121469    .2183823
       numsq |   .0038339   .0316111     0.12   0.903    -.0581227    .0657905
   numsq_con |  -.0498926   .0323761    -1.54   0.123    -.1133486    .0135633
   incentive |   -.069033   .1518841    -0.45   0.649    -.3667203    .2286543
      in_con |  -.1383909   .1575835    -0.88   0.380    -.4472488    .1704671
      in_num |   .0600729   .0707692     0.85   0.396    -.0786322     .198778
    in_numsq |   .0112619   .0390023     0.29   0.773    -.0651812    .0877051
  in_num_con |  -.0028927   .0729311    -0.04   0.968    -.1458351    .1400497
in_numsq_con |   .0527369    .040643     1.30   0.194    -.0269219    .1323958
       _cons |  -.1518937   .1240183    -1.22   0.221    -.3949651    .0911777
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.282 congenial 1 num_con 3.282 numsq 10.772 numsq_con 10.772 inc
> entive 1 in_con 1 in_num 3.282 in_numsq 10.772 in_num_con 3.282 in_numsq_con 10
> .772 if order_num_treat == 1

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.282 -3.282 numsq_con 10.7
> 72 -10.772 in_con 1 -1 in_num_con 3.282 -3.282 in_numsq_con 10.772 -10.772) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .3455946      .064812     .2251139    .4856041
             Pr(correct=1) |   .6544054      .064812     .5143959    .7748861

First Difference: congenial 1  -1 num_con 3.282 -3.282 numsq_con 10.772 -10.772 i
> n_con 1 -1 in_num_con 3.282 -3.282 in_numsq_con 10.772 -10.772

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.2014686     .1015867    -.4033174   -.0038403

. drop b*

. *------------------------------------------------------------------------------
> -
. ****The results from the t-test below are used to create Table A24 manually in 
> latex.
. *------------------------------------------------------------------------------
> -
. *Simulation1/2 SD1 No-incentive - Low vs High Numeracy
. ttesti 1000 .0536047 2.103876  1000 -.1161485 2.11446  

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0536047    .0665304    2.103876   -.0769507    .1841601
       y |   1,000   -.1161485    .0668651     2.11446   -.2473607    .0150637
---------+--------------------------------------------------------------------
Combined |   2,000   -.0312719     .047189    2.110355   -.1238166    .0612728
---------+--------------------------------------------------------------------
    diff |            .1697532    .0943252               -.0152328    .3547392
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.7997
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9640         Pr(|T| > |t|) = 0.0721          Pr(T > t) = 0.0360

. 
. *Simulation3/4 SD1 Incentive - Low vs High Numeracy
. ttesti 1000 .0471925 1.464353  1000 -.1137994 1.484079

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0471925    .0463069    1.464353   -.0436775    .1380625
       y |   1,000   -.1137994    .0469307    1.484079   -.2058935   -.0217053
---------+--------------------------------------------------------------------
Combined |   2,000   -.0333034    .0330061    1.476078   -.0980334    .0314265
---------+--------------------------------------------------------------------
    diff |            .1609919    .0659304                .0316923    .2902915
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.4418
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9927         Pr(|T| > |t|) = 0.0147          Pr(T > t) = 0.0073

. 
. *Simulation5/6 SD1.5 No-incentive - Low vs High Numeracy
. ttesti 1000 .1755068 3.487493  1000 -.0745441 2.754565

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .1755068    .1102842    3.487493   -.0409085    .3919221
       y |   1,000   -.0745441     .087107    2.754565   -.2454778    .0963896
---------+--------------------------------------------------------------------
Combined |   2,000    .0504814    .0703058    3.144172    -.087399    .1883617
---------+--------------------------------------------------------------------
    diff |            .2500509    .1405355               -.0255606    .5256624
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.7793
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9623         Pr(|T| > |t|) = 0.0753          Pr(T > t) = 0.0377

. 
. *Simulation7/8 SD1.5 Incentive - Low vs High Numeracy
. ttesti 1000 .0800150 2.51796  1000 -.1588158 2.001219

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000     .080015    .0796249     2.51796   -.0762362    .2362662
       y |   1,000   -.1588158    .0632841    2.001219   -.2830008   -.0346308
---------+--------------------------------------------------------------------
Combined |   2,000   -.0394004    .0509126    2.276879   -.1392477    .0604469
---------+--------------------------------------------------------------------
    diff |            .2388308    .1017104                .0393613    .4383003
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.3481
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9905         Pr(|T| > |t|) = 0.0190          Pr(T > t) = 0.0095

. 
. *Simulation9/10 SD2 No-incentive - Low vs High Numeracy
. ttesti 1000 .3118046 5.314862  1000 .0001605 4.315826

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .3118046    .1680707    5.314862   -.0180075    .6416167
       y |   1,000    .0001605    .1364784    4.315826   -.2676567    .2679777
---------+--------------------------------------------------------------------
Combined |   2,000    .1559825    .1082812    4.842481   -.0563732    .3683383
---------+--------------------------------------------------------------------
    diff |            .3116441    .2165043               -.1129537    .7362419
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.4394
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9249         Pr(|T| > |t|) = 0.1502          Pr(T > t) = 0.0751

. 
. *Simulation11/12 SD2 Incentive - Low vs High Numeracy
. ttesti 1000 .108679 4.203793  1000 -.2014686 3.212454

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000     .108679    .1329356    4.203793   -.1521861    .3695441
       y |   1,000   -.2014686    .1015867    3.212454   -.4008164   -.0021208
---------+--------------------------------------------------------------------
Combined |   2,000   -.0463948    .0837046    3.743384   -.2105522    .1177626
---------+--------------------------------------------------------------------
    diff |            .3101476    .1673073               -.0179675    .6382627
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.8538
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9680         Pr(|T| > |t|) = 0.0639          Pr(T > t) = 0.0320

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Analysis with no deviations from pre-registration
. * Multivariate analyses
. * Table A25: The impact of numeracy and congeniality on accuracy (unincentivize
> d)
. * Table A26: The impact of incentives, numeracy and congeneity on accuracy (all
> )
. * Figure A5: Predicted probabilities of correctly interpreting the data
. * Table A27: Difference in the exhibited congeniality bias
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A25: The impact of numeracy and congeniality on accuracy (unincentivize
> d)
. *------------------------------------------------------------------------------
> -
. * Equation 1 (without control variables) - Table A25 (1)
. reg correct numeracy congenial num_con numsq if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(4, 1011)        =       3.23
                                                Prob > F          =     0.0121
                                                R-squared         =     0.0124
                                                Root MSE          =     .49222

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0045403    .009619    -0.47   0.637    -.0234158    .0143352
   congenial |   .0465499   .0155106     3.00   0.003     .0161133    .0769866
     num_con |   .0153887   .0093316     1.65   0.099    -.0029229    .0337002
       numsq |   .0035025   .0053361     0.66   0.512    -.0069686    .0139735
       _cons |   .4135609   .0212349    19.48   0.000     .3718913    .4552304
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A25 (2)
. reg correct numeracy congenial num_con numsq age i.gender i.race i.edu i.vote20
> 16 if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(24, 991)        =       1.85
                                                Prob > F          =     0.0078
                                                R-squared         =     0.0389
                                                Root MSE          =     .49045

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
      numeracy |  -.0056391   .0103934    -0.54   0.588    -.0260347    .0147566
     congenial |   .0432262   .0156573     2.76   0.006     .0125008    .0739515
       num_con |   .0128379   .0094456     1.36   0.174    -.0056977    .0313736
         numsq |   .0047846   .0054081     0.88   0.377     -.005828    .0153972
           age |   .0012916    .001026     1.26   0.208    -.0007218     .003305
               |
        gender |
         Male  |   .0294365   .0332124     0.89   0.376    -.0357383    .0946113
        Other  |   .0798499   .3145889     0.25   0.800     -.537487    .6971868
      Not say  |  -.0905611   .3533947    -0.26   0.798     -.784049    .6029268
               |
          race |
Non-hispani..  |   .0860694   .0768006     1.12   0.263    -.0646411    .2367799
     Hispanic  |   .1360573   .0455747     2.99   0.003     .0466233    .2254913
        Asian  |   .1409327   .0796824     1.77   0.077    -.0154329    .2972982
American In..  |  -.1912952   .1599797    -1.20   0.232     -.505233    .1226426
       Others  |   .0808856   .0994371     0.81   0.416     -.114246    .2760171
Prefer not ..  |   .1916552   .1486129     1.29   0.197    -.0999769    .4832872
               |
           edu |
High school..  |  -.0526037   .0783293    -0.67   0.502    -.2063141    .1011067
 Some college  |  -.1241694   .0800114    -1.55   0.121    -.2811806    .0328418
 College grad  |  -.1214865   .0817711    -1.49   0.138    -.2819509    .0389779
    Post grad  |   -.041777   .0869037    -0.48   0.631    -.2123134    .1287595
        Other  |  -.2513407   .1708048    -1.47   0.141    -.5865212    .0838399
               |
      vote2016 |
      Clinton  |  -.0423941   .0400486    -1.06   0.290    -.1209838    .0361957
Other candi..  |   .0667323   .0775465     0.86   0.390    -.0854418    .2189065
      No vote  |  -.0592206   .0459442    -1.29   0.198    -.1493796    .0309385
      Not say  |   .0697485   .0931761     0.75   0.454    -.1130965    .2525936
        Other  |  -.0067691   .1744365    -0.04   0.969    -.3490764    .3355383
               |
         _cons |   .4012282   .1014001     3.96   0.000     .2022446    .6002117
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Export Table A25 in Latex
. esttab  a1 a2 using "${main_appendix}/Table_A25.tex" ,  ///
>                 nonumbers  b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Testing Hypotheses 1 and 2) replace       ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes(Note:Linear Probability Model with heterscedastici
> ty robust standard errors.)
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A25.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A26: The impact of incentives, numeracy and congeneity on accuracy (all
> )
. *------------------------------------------------------------------------------
> - 
. * Equation 2 (without control variables) - Table A26 (3)
. reg correct incentive, r

Linear regression                               Number of obs     =      3,050
                                                F(1, 3048)        =       0.01
                                                Prob > F          =     0.9412
                                                R-squared         =     0.0000
                                                Root MSE          =     .49409

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |  -.0013994   .0189843    -0.07   0.941    -.0386228    .0358239
       _cons |   .4232283   .0155055    27.30   0.000     .3928261    .4536306
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table A26 (4)
. reg correct incentive age i.gender i.race i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(21, 3028)       =       1.38
                                                Prob > F          =     0.1160
                                                R-squared         =     0.0092
                                                Root MSE          =     .49344

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |  -.0018305   .0189514    -0.10   0.923    -.0389896    .0353285
           age |   .0003372   .0005951     0.57   0.571    -.0008296     .001504
               |
        gender |
         Male  |   .0396994   .0186028     2.13   0.033      .003224    .0761748
        Other  |  -.0710805   .1835674    -0.39   0.699    -.4310098    .2888489
      Not say  |   .2250088   .1773961     1.27   0.205    -.1228203    .5728378
               |
          race |
Non-hispani..  |    .033006   .0420589     0.78   0.433    -.0494609    .1154728
     Hispanic  |   .0547986   .0275072     1.99   0.046      .000864    .1087333
        Asian  |    .041658    .042932     0.97   0.332    -.0425207    .1258368
American In..  |  -.0310012   .1251877    -0.25   0.804    -.2764628    .2144604
       Others  |    .003936   .0594216     0.07   0.947    -.1125747    .1204468
Prefer not ..  |   .0453473   .0866308     0.52   0.601    -.1245138    .2152084
               |
           edu |
High school..  |  -.0017768   .0499827    -0.04   0.972    -.0997801    .0962266
 Some college  |  -.0421486    .051065    -0.83   0.409    -.1422743     .057977
 College grad  |  -.0463904    .051835    -0.89   0.371    -.1480259     .055245
    Post grad  |   .0293679   .0543959     0.54   0.589    -.0772887    .1360245
        Other  |  -.1762801   .1073709    -1.64   0.101    -.3868073     .034247
               |
      vote2016 |
      Clinton  |   .0087136   .0229911     0.38   0.705    -.0363661    .0537933
Other candi..  |   .0316978   .0437519     0.72   0.469    -.0540887    .1174843
      No vote  |  -.0321485   .0265273    -1.21   0.226     -.084162    .0198649
      Not say  |   .0245996   .0528824     0.47   0.642    -.0790895    .1282886
        Other  |   .1076193   .1187254     0.91   0.365    -.1251713    .3404099
               |
         _cons |   .3969256   .0626795     6.33   0.000      .274027    .5198243
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Equation 3 (without control variables) - Table A26 (5)
. reg correct numeracy congenial num_con numsq incentive in_con in_num in_num_con
> , r

Linear regression                               Number of obs     =      3,050
                                                F(8, 3041)        =       4.09
                                                Prob > F          =     0.0001
                                                R-squared         =     0.0108
                                                Root MSE          =     .49199

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0048047   .0094264    -0.51   0.610    -.0232875    .0136781
   congenial |   .0465206   .0154903     3.00   0.003      .016148    .0768931
     num_con |   .0154227   .0093189     1.65   0.098    -.0028493    .0336947
       numsq |   .0041249   .0030636     1.35   0.178    -.0018821    .0101318
   incentive |  -.0017817    .018895    -0.09   0.925    -.0388301    .0352666
      in_con |  -.0262035   .0189647    -1.38   0.167    -.0633885    .0109814
      in_num |    .021161   .0114501     1.85   0.065    -.0012898    .0436117
  in_num_con |   .0012603   .0113953     0.11   0.912     -.021083    .0236035
       _cons |   .4118502   .0175505    23.47   0.000     .3774381    .4462623
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A26 (6)
. reg correct numeracy congenial num_con numsq incentive in_con in_num in_num_con
>  age i.gender i.race i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(28, 3021)       =       2.09
                                                Prob > F          =     0.0007
                                                R-squared         =     0.0187
                                                Root MSE          =     .49163

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
      numeracy |  -.0068381   .0096599    -0.71   0.479    -.0257788    .0121026
     congenial |   .0448449   .0154613     2.90   0.004     .0145292    .0751605
       num_con |   .0137171   .0093467     1.47   0.142    -.0046095    .0320437
         numsq |     .00415   .0030812     1.35   0.178    -.0018916    .0101915
     incentive |  -.0017327   .0188769    -0.09   0.927    -.0387456    .0352801
        in_con |  -.0249766    .018958    -1.32   0.188    -.0621484    .0121952
        in_num |   .0203337   .0114994     1.77   0.077    -.0022137     .042881
    in_num_con |   .0032837   .0114488     0.29   0.774    -.0191645    .0257318
           age |   .0003235   .0005929     0.55   0.585    -.0008391    .0014861
               |
        gender |
         Male  |   .0342311   .0187878     1.82   0.069    -.0026071    .0710693
        Other  |  -.0724242   .1804742    -0.40   0.688    -.4262889    .2814404
      Not say  |   .2279237   .1794439     1.27   0.204    -.1239209    .5797683
               |
          race |
Non-hispani..  |   .0349321   .0427421     0.82   0.414    -.0488744    .1187386
     Hispanic  |   .0541001   .0273986     1.97   0.048     .0003784    .1078219
        Asian  |   .0381029   .0430472     0.89   0.376    -.0463018    .1225077
American In..  |  -.0433868   .1278783    -0.34   0.734     -.294124    .2073505
       Others  |   .0054558   .0585375     0.09   0.926    -.1093215    .1202331
Prefer not ..  |   .0457748   .0866949     0.53   0.598    -.1242121    .2157617
               |
           edu |
High school..  |  -.0038406   .0500193    -0.08   0.939    -.1019159    .0942347
 Some college  |  -.0483186   .0511627    -0.94   0.345    -.1486357    .0519986
 College grad  |  -.0522511   .0521062    -1.00   0.316    -.1544182    .0499161
    Post grad  |   .0142482   .0547356     0.26   0.795    -.0930747    .1215711
        Other  |  -.1750371   .1062797    -1.65   0.100     -.383425    .0333507
               |
      vote2016 |
      Clinton  |    .003171   .0229208     0.14   0.890    -.0417709    .0481129
Other candi..  |   .0202353   .0439757     0.46   0.645    -.0659901    .1064607
      No vote  |  -.0367212   .0264703    -1.39   0.165    -.0886229    .0151805
      Not say  |   .0181977   .0530588     0.34   0.732    -.0858373    .1222326
        Other  |    .117697    .117753     1.00   0.318    -.1131872    .3485812
               |
         _cons |   .3985404   .0633888     6.29   0.000     .2742509    .5228298
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Export Table A26 in Latex
. esttab  a3 a4 a5 a6 using "${main_appendix}/Table_A26.tex" ,  ///
>                 nonumbers  b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Testing Hypothesis 3 and 4) replace       ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes(Note:Linear Probability Model with heterscedastici
> ty robust standard errors.)
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A26.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A5: Predicted probabilities of correctly interpreting the data
. *------------------------------------------------------------------------------
> -
. * GRAPH1: TOP-LEFT Graph (Non-incentivized & Low numeracy)
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.654, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4107253     .0319329     .3527101    .4778748

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4536799     .0306598     .3918975    .5125065

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 0 num_con 0 numsq 2.736 incentive 0 in_con 0 in_
> num 0 in_num_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4314433     .0221903     .3866946    .4749631

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4107253    .0319329   .3217001   .5394965
          p2 |      1,000    .4536799    .0306598   .3558929   .5545364
          p3 |      1,000    .4314433    .0221903   .3595441   .5112336

. *-------------------------------------------------------GRAPH1-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.33 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.54 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (16 0.50 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(large))                                                                 
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("Low numeracy", size (large))            
>                                                                                
>                                                           ///
>                                 name(topleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH2: TOP-RIGHT Graph (Non-incentivized & High numeracy)
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=+1.654, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3446103     .0304704     .2857846    .4043766

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 incentive 0 in_con 0 
> in_num 0 in_num_con 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4880752     .0315772     .4253271     .551921

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 0 num_con 0 numsq 2.736 incentive 0 in_con 0 in_n
> um 0 in_num_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4122986     .0227808     .3675595    .4571477

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3446103    .0304704   .2471689   .4617261
          p2 |      1,000    .4880752    .0315772   .3867155   .5876409
          p3 |      1,000    .4122986    .0227808   .3436538   .4983326

. 
. *-------------------------------------------------------GRAPH2-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(9 0.26 "Cong
> enial = -1", color (orange) size(small)))        ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(13.5 0.52 "Congenial = +1", color (green) size(small)))       /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (18 0.47 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("High numeracy", size (large))           
>                                                                                
>                                                   ///
>                                 name(topright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH3: BOTTOM-LEFT Graph (Incentivized & Low numeracy)
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.654, incentive =1
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 incentive 1 in_con 
> -1 in_num -1.654 in_num_con 1.654

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4021216     .0225543     .3586027    .4440971

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 incentive 1 in_con 
> 1 in_num -1.654 in_num_con -1.654

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3877777     .0214994     .3456698    .4309684

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 0 num_con 0 numsq 2.736 incentive 1 in_con 0 in_
> num -1.654 in_num_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3937021     .0158994     .3647942    .4260391

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4021216    .0225543   .3364587   .4813414
          p2 |      1,000    .3877777    .0214994   .3249658   .4477268
          p3 |      1,000    .3937021    .0158994   .3505142   .4517949

. *-------------------------------------------------------GRAPH3-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(9 0.49 "Cong
> enial = -1", color (orange) size(small)))        ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.30 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (21 0.46 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("  Incentivized  ", orientation(vertical
> ) size(large))                                                                 
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH4: BOTTOM-RIGHT Graph (Incentivized & High numeracy)
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs.*/
. * High Numeracy, Incentive=1*/
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=1.654, incentive =1*/
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 incentive 1 in_con 
> -1 in_num 1.654 in_num_con -1.654

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .400394     .0212904     .3588936    .4429649

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 incentive 1 in_con 1 
> in_num 1.654 in_num_con 1.654

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4960233     .0216527     .4544073    .5378314

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 0 num_con 0 numsq 2.736 incentive 1 in_con 0 in_n
> um 1.654 in_num_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4478025     .0162984       .41318    .4809709

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000     .400394    .0212904   .3141576   .4878258
          p2 |      1,000    .4960233    .0216527    .431208    .559765
          p3 |      1,000    .4478025    .0162984   .3982156   .4985859

. *-------------------------------------------------------GRAPH4-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.32 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(19 0.54 "Congenial = +1", color (green) size(small)))         /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (23 0.51 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft1 topright1 botleft1 botright1, scheme(plotplain)

. graph export "${main_appendix}/Figure_A5.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A5.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A27: Difference in the exhibited congeniality bias
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> *
. * Model SD 1
. *******************************************************************************
> *
. * Simulation 1
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -1.654
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1) = C
> ongeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5477978     .0310719     .4859245    .6075477
             Pr(correct=1) |   .4522022     .0310719     .3924523    .5140755

First Difference: congenial 1  -1 num_con -1.654 1.654

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0414919     .0444289    -.1277574    .0489727

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 2
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 1.654
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 incentive 0 in_con 0 
> in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5119575     .0318114     .4510081    .5742473
             Pr(correct=1) |   .4880425     .0318114     .4257527    .5489919

First Difference: congenial 1  -1 num_con 1.654 -1.654

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |    -.14596     .0459967    -.2346095   -.0583467

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 3
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -1.654
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 incentive 1 in_con 
> 1 in_num -1.654 in_num_con -1.654

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654 in_con 1 -1 in
> _num_con -1.654 1.654) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6129155     .0220592       .57022    .6560077
             Pr(correct=1) |   .3870845     .0220592     .3439923      .42978

First Difference: congenial 1  -1 num_con -1.654 1.654 in_con 1 -1 in_num_con -1.
> 654 1.654

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0148144     .0311439    -.0445052    .0749395

. drop b*

. *******************************************************************************
> ****************************************
. * Simulation 4
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 1.654
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 incentive 1 in_con 1 
> in_num 1.654 in_num_con 1.654

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654 in_con 1 -1 in
> _num_con 1.654 -1.654) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5032798     .0225398     .4588027    .5454549
             Pr(correct=1) |   .4967202     .0225398     .4545451    .5411973

First Difference: congenial 1  -1 num_con 1.654 -1.654 in_con 1 -1 in_num_con 1.6
> 54 -1.654

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0973284     .0312508    -.1608236   -.0373754

. drop b*

. *******************************************************************************
> *
. *Model SD 1.5
. *******************************************************************************
> *
. * Simulation 5
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -2.481
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -2.481 congenial 1 num_con -2.481 numsq 6.155 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.481 2.481) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5428844      .041517     .4589061    .6224672
             Pr(correct=1) |   .4571156      .041517     .3775328    .5410939

First Difference: congenial 1  -1 num_con -2.481 2.481

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0147676      .057786    -.1300986    .1000458

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 6
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 2.481
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 2.481 congenial 1 num_con 2.481 numsq 6.155 incentive 0 in_con 0 
> in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.481 -2.481) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4891793     .0415728     .4117914    .5715074
             Pr(correct=1) |   .5108207     .0415728     .4284926    .5882086

First Difference: congenial 1  -1 num_con 2.481 -2.481

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1723222     .0587521    -.2840942   -.0602123

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 7
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -2.481
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -2.481 congenial 1 num_con -2.481 numsq 6.155 incentive 1 in_con 
> 1 in_num -2.481 in_num_con -2.481

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.481 2.481 in_con 1 -1 in
> _num_con -2.481 2.481) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .625922     .0307369      .565267    .6872927
             Pr(correct=1) |    .374078     .0307369     .3127073     .434733

First Difference: congenial 1  -1 num_con -2.481 2.481 in_con 1 -1 in_num_con -2.
> 481 2.481

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0420155     .0395033     -.034662    .1182435

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 8
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy= 2.481
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 2.481 congenial 1 num_con 2.481 numsq 6.155 incentive 1 in_con 1 
> in_num 2.481 in_num_con 2.481

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.481 -2.481 in_con 1 -1 in
> _num_con 2.481 -2.481) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4616562     .0287673      .409517    .5165554
             Pr(correct=1) |   .5383438     .0287673     .4834446     .590483

First Difference: congenial 1  -1 num_con 2.481 -2.481 in_con 1 -1 in_num_con 2.4
> 81 -2.481

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1261209     .0398513    -.2054318   -.0502784

. drop b*

. *******************************************************************************
> *
. *Model SD 2
. *******************************************************************************
> *
. * Simulation 9
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy= -3.308
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -3.308 congenial 1 num_con -3.308 numsq 10.943 incentive 0 in_con
>  0 in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.308 3.308) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5324164     .0562558     .4228555    .6370521
             Pr(correct=1) |   .4675836     .0562558     .3629479    .5771445

First Difference: congenial 1  -1 num_con -3.308 3.308

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0122335     .0724664      -.13156    .1553185

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 10
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy= 3.308
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)= Co
> ngeniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 3.308 congenial 1 num_con 3.308 numsq 10.943 incentive 0 in_con 0
>  in_num 0 in_num_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.308 -3.308) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4611908     .0549644     .3612014     .570599
             Pr(correct=1) |   .5388092     .0549644      .429401    .6387986

First Difference: congenial 1  -1 num_con 3.308 -3.308

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1985691     .0725285    -.3359013   -.0567016

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 11
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -3.308
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -3.308 congenial 1 num_con -3.308 numsq 10.943 incentive 1 in_con
>  1 in_num -3.308 in_num_con -3.308

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.308 3.308 in_con 1 -1 in
> _num_con -3.308 3.308) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6332595     .0441449      .545955    .7194045
             Pr(correct=1) |   .3667405     .0441449     .2805954     .454045

First Difference: congenial 1  -1 num_con -3.308 3.308 in_con 1 -1 in_num_con -3.
> 308 3.308

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |    .069221     .0488507    -.0277394    .1602931

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 12
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 3.308
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)= Con
> geniality bias
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 3.308 congenial 1 num_con 3.308 numsq 10.943 incentive 1 in_con 1
>  in_num 3.308 in_num_con 3.308

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.308 -3.308 in_con 1 -1 in
> _num_con 3.308 -3.308) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4154214     .0388213     .3440858    .4951063
             Pr(correct=1) |   .5845786     .0388213     .5048937    .6559142

First Difference: congenial 1  -1 num_con 3.308 -3.308 in_con 1 -1 in_num_con 3.3
> 08 -3.308

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1539165     .0490776    -.2530299   -.0601573

. drop b*

. 
. *------------------------------------------------------------------------------
> -
. ****The results from the t-test below are used to create Table A27 manually in 
> latex.
. *------------------------------------------------------------------------------
> -
. 
. *Simulation1/2 SD1 No-incentive - Low vs High Numeracy
. ttesti 1000  -.0414919 1.4049751  1000 -.14596 1.4545536

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0414919    .0444292    1.404975   -.1286772    .0456934
       y |   1,000     -.14596     .045997    1.454554   -.2362219   -.0556981
---------+--------------------------------------------------------------------
Combined |   2,000    -.093726    .0319886    1.430576   -.1564605   -.0309914
---------+--------------------------------------------------------------------
    diff |            .1044681    .0639506               -.0209488     .229885
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.6336
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9487         Pr(|T| > |t|) = 0.1025          Pr(T > t) = 0.0513

. 
. *Simulation3/4 SD1 Incentive - Low vs High Numeracy
. ttesti 1000 .0148144 .98486355  1000 -.0973284  .98824405

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0148144    .0311441    .9848636    -.046301    .0759298
       y |   1,000   -.0973284     .031251    .9882441   -.1586536   -.0360032
---------+--------------------------------------------------------------------
Combined |   2,000    -.041257    .0220902    .9879018   -.0845791    .0020651
---------+--------------------------------------------------------------------
    diff |            .1121428    .0441201                .0256166     .198669
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.5418
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9944         Pr(|T| > |t|) = 0.0111          Pr(T > t) = 0.0056

. 
. *Simulation5/6 SD1.5 No-incentive - Low vs High Numeracy
. ttesti 1000  -.0147676 1.82735  1000 -.1723222 1.8579045

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0147676    .0577859     1.82735   -.1281632     .098628
       y |   1,000   -.1723222    .0587521    1.857905   -.2876139   -.0570305
---------+--------------------------------------------------------------------
Combined |   2,000   -.0935449    .0412312    1.843914   -.1744055   -.0126843
---------+--------------------------------------------------------------------
    diff |            .1575546    .0824076               -.0040593    .3191685
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.9119
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9720         Pr(|T| > |t|) = 0.0560          Pr(T > t) = 0.0280

. 
. *Simulation7/8 SD1.5 Incentive - Low vs High Numeracy
. ttesti 1000 .0420155 1.2492040  1000 -.1261209  1.2602088

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0420155    .0395033    1.249204   -.0355035    .1195345
       y |   1,000   -.1261209    .0398513    1.260209   -.2043228    -.047919
---------+--------------------------------------------------------------------
Combined |   2,000   -.0420527    .0281123     1.25722   -.0971852    .0130798
---------+--------------------------------------------------------------------
    diff |            .1681364    .0561127                .0580908     .278182
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.9964
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9986         Pr(|T| > |t|) = 0.0028          Pr(T > t) = 0.0014

. 
. *Simulation9/10 SD2 No-incentive - Low vs High Numeracy
. ttesti 1000 .0122335 2.2915888  1000 -.1985691 2.2935526

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0122335    .0724664    2.291589   -.1299703    .1544373
       y |   1,000   -.1985691    .0725285    2.293553   -.3408948   -.0562434
---------+--------------------------------------------------------------------
Combined |   2,000   -.0931678    .0513048    2.294421   -.1937843    .0074487
---------+--------------------------------------------------------------------
    diff |            .2108026    .1025269                .0097318    .4118734
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.0561
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9800         Pr(|T| > |t|) = 0.0399          Pr(T > t) = 0.0200

. 
. *Simulation11/12 SD2 Incentive - Low vs High Numeracy
. ttesti 1000 .069221 1.5447948  1000 -.1539165 1.5519699

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000     .069221    .0488507    1.544795   -.0266408    .1650828
       y |   1,000   -.1539165    .0490776     1.55197   -.2502235   -.0576095
---------+--------------------------------------------------------------------
Combined |   2,000   -.0423478    .0347041    1.552017   -.1104078    .0257123
---------+--------------------------------------------------------------------
    diff |            .2231375    .0692459                .0873357    .3589393
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   3.2224
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9994         Pr(|T| > |t|) = 0.0013          Pr(T > t) = 0.0006

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Analysis with no deviations from pre-registration
. * Logistic regression
. * Table A28: The impact of numeracy and congeniality on accuracy (H1&H2)
. * Table A29: The impact of numeracy and congeniality on accuracy (H3&H4)
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A28: The impact of numeracy and congeniality on accuracy (H1&H2)
. *------------------------------------------------------------------------------
> -
. * Equation 1 (without control variables) - Table A28 (1)
. logit correct numeracy congenial num_con numsq if incentive==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -685.86665  
Iteration 2:   log pseudolikelihood = -685.86053  
Iteration 3:   log pseudolikelihood = -685.86053  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(4)  =  12.08
                                                        Prob > chi2   = 0.0168
Log pseudolikelihood = -685.86053                       Pseudo R2     = 0.0092

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0206545    .039706    -0.52   0.603    -.0984768    .0571679
   congenial |   .1938244   .0651561     2.97   0.003     .0661208     .321528
     num_con |   .0651274   .0397656     1.64   0.101    -.0128117    .1430665
       numsq |   .0139958    .022079     0.63   0.526    -.0292781    .0572698
       _cons |    -.35236    .088103    -4.00   0.000    -.5250387   -.1796813
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table A28 (2)
. logit correct numeracy congenial num_con numsq age i.gender i.race i.edu i.vote
> 2016 if incentive==0, r

Iteration 0:   log pseudolikelihood = -692.21365  
Iteration 1:   log pseudolikelihood = -672.14203  
Iteration 2:   log pseudolikelihood = -672.06916  
Iteration 3:   log pseudolikelihood = -672.06898  
Iteration 4:   log pseudolikelihood = -672.06898  

Logistic regression                                     Number of obs =  1,016
                                                        Wald chi2(24) =  38.30
                                                        Prob > chi2   = 0.0323
Log pseudolikelihood = -672.06898                       Pseudo R2     = 0.0291

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
      numeracy |   -.025961   .0435497    -0.60   0.551    -.1113168    .0593947
     congenial |   .1842563    .066643     2.76   0.006     .0536383    .3148742
       num_con |   .0558495   .0407235     1.37   0.170    -.0239672    .1356661
         numsq |   .0200756   .0227184     0.88   0.377    -.0244518    .0646029
           age |   .0054995   .0043367     1.27   0.205    -.0030003    .0139992
               |
        gender |
         Male  |   .1254854   .1396787     0.90   0.369    -.1482799    .3992507
        Other  |   .3359386   1.257496     0.27   0.789    -2.128708    2.800585
      Not say  |  -.3787907   1.424808    -0.27   0.790    -3.171363    2.413782
               |
          race |
Non-hispani..  |   .3612902   .3138693     1.15   0.250    -.2538824    .9764627
     Hispanic  |   .5699133   .1897828     3.00   0.003     .1979457    .9418808
        Asian  |   .5914841   .3287841     1.80   0.072    -.0529208    1.235889
American In..  |  -1.030546   1.115105    -0.92   0.355    -3.216111    1.155019
       Others  |   .3440653   .4073499     0.84   0.398    -.4543257    1.142456
Prefer not ..  |   .8025142   .6237818     1.29   0.198    -.4200757    2.025104
               |
           edu |
High school..  |  -.2182614    .319327    -0.68   0.494    -.8441308    .4076081
 Some college  |  -.5223759   .3301297    -1.58   0.114    -1.169418    .1246665
 College grad  |  -.5092395    .335983    -1.52   0.130    -1.167754    .1492751
    Post grad  |   -.176526   .3553921    -0.50   0.619    -.8730817    .5200297
        Other  |  -1.156928   .9031201    -1.28   0.200    -2.927011    .6131549
               |
      vote2016 |
      Clinton  |  -.1789468   .1691255    -1.06   0.290    -.5104267    .1525332
Other candi..  |   .2752523   .3161208     0.87   0.384    -.3443332    .8948377
      No vote  |  -.2482769   .1942134    -1.28   0.201    -.6289282    .1323744
      Not say  |     .28897    .381255     0.76   0.448    -.4582761    1.036216
        Other  |  -.0081709   .7171826    -0.01   0.991    -1.413823    1.397481
               |
         _cons |  -.4174081   .4209476    -0.99   0.321     -1.24245     .407634
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Export Table A28 in Latex
. esttab  a1 a2 using "${main_appendix}/Table_A28.tex" ,  ///
>             b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Testing Hypotheses 1 and 2) replace       ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes(Note:Logit regression with heterscedasticity robus
> t standard errors.)
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A28.tex)

. eststo clear    

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table A29: The impact of numeracy and congeniality on accuracy (H3&H4)
. *------------------------------------------------------------------------------
> -
. * Equation 2 (without control variables) - Table A29 (3)
. logit correct incentive, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2077.1143  
Iteration 2:   log pseudolikelihood = -2077.1143  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(1)  =   0.01
                                                        Prob > chi2   = 0.9412
Log pseudolikelihood = -2077.1143                       Pseudo R2     = 0.0000

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |  -.0057354    .077781    -0.07   0.941    -.1581835    .1467126
       _cons |  -.3095346    .063509    -4.87   0.000    -.4340099   -.1850593
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table A29 (4)
. logit correct incentive age i.gender i.race i.edu i.vote2016, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2063.0942  
Iteration 2:   log pseudolikelihood = -2063.0836  
Iteration 3:   log pseudolikelihood = -2063.0836  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(21) =  27.77
                                                        Prob > chi2   = 0.1468
Log pseudolikelihood = -2063.0836                       Pseudo R2     = 0.0068

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |  -.0070454   .0781388    -0.09   0.928    -.1601945    .1461037
           age |   .0014021   .0024559     0.57   0.568    -.0034113    .0062156
               |
        gender |
         Male  |   .1637638   .0765585     2.14   0.032     .0137119    .3138157
        Other  |  -.3060898   .8296312    -0.37   0.712    -1.932137    1.319958
      Not say  |   .9330308   .7723567     1.21   0.227    -.5807606    2.446822
               |
          race |
Non-hispani..  |   .1361987   .1718378     0.79   0.428    -.2005972    .4729946
     Hispanic  |    .226152     .11278     2.01   0.045     .0051073    .4471967
        Asian  |   .1713442   .1750056     0.98   0.328    -.1716603    .5143488
American In..  |  -.1336213   .5462036    -0.24   0.807    -1.204161     .936918
       Others  |   .0164908    .247544     0.07   0.947    -.4686865     .501668
Prefer not ..  |   .1876689    .355086     0.53   0.597    -.5082868    .8836246
               |
           edu |
High school..  |   -.007694   .2062698    -0.04   0.970    -.4119755    .3965875
 Some college  |  -.1750584   .2113815    -0.83   0.408    -.5893585    .2392418
 College grad  |  -.1918898   .2142556    -0.90   0.370    -.6118231    .2280434
    Post grad  |   .1165934   .2234095     0.52   0.602    -.3212813     .554468
        Other  |  -.7817565   .5188701    -1.51   0.132    -1.798723    .2352101
               |
      vote2016 |
      Clinton  |   .0358048   .0942219     0.38   0.704    -.1488667    .2204762
Other candi..  |   .1295972   .1775493     0.73   0.465     -.218393    .4775873
      No vote  |  -.1340218   .1102528    -1.22   0.224    -.3501134    .0820697
      Not say  |   .1014171   .2155936     0.47   0.638    -.3211386    .5239727
        Other  |   .4415224   .4827597     0.91   0.360    -.5046693    1.387714
               |
         _cons |  -.4194946   .2588283    -1.62   0.105    -.9267887    .0877996
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Equation 3 (without control variables) - Table A29 (5)
. logit correct numeracy congenial num_con numsq incentive in_con in_num in_num_c
> on, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2060.7422  
Iteration 2:   log pseudolikelihood =  -2060.735  
Iteration 3:   log pseudolikelihood =  -2060.735  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(8)  =  31.32
                                                        Prob > chi2   = 0.0001
Log pseudolikelihood = -2060.735                        Pseudo R2     = 0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table A29 (6)
. logit correct numeracy congenial num_con numsq incentive in_con in_num in_num_c
> on age i.gender i.race i.edu i.vote2016, r

Iteration 0:   log pseudolikelihood = -2077.1171  
Iteration 1:   log pseudolikelihood = -2048.4917  
Iteration 2:   log pseudolikelihood = -2048.4668  
Iteration 3:   log pseudolikelihood = -2048.4668  

Logistic regression                                     Number of obs =  3,050
                                                        Wald chi2(28) =  54.55
                                                        Prob > chi2   = 0.0019
Log pseudolikelihood = -2048.4668                       Pseudo R2     = 0.0138

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
      numeracy |  -.0302985   .0403045    -0.75   0.452    -.1092938    .0486968
     congenial |   .1881378   .0652206     2.88   0.004     .0603077    .3159679
       num_con |   .0587007   .0399879     1.47   0.142    -.0196742    .1370755
         numsq |   .0168639   .0128036     1.32   0.188    -.0082307    .0419586
     incentive |  -.0043408   .0786457    -0.06   0.956    -.1584835    .1498019
        in_con |  -.1066528   .0796848    -1.34   0.181    -.2628322    .0495266
        in_num |   .0854978   .0479826     1.78   0.075    -.0085464    .1795421
    in_num_con |   .0112388   .0486531     0.23   0.817    -.0841196    .1065972
           age |   .0013609   .0024666     0.55   0.581    -.0034735    .0061953
               |
        gender |
         Male  |   .1426047   .0779691     1.83   0.067     -.010212    .2954214
        Other  |   -.319391   .8269584    -0.39   0.699      -1.9402    1.301418
      Not say  |   .9462818   .7786682     1.22   0.224    -.5798798    2.472443
               |
          race |
Non-hispani..  |   .1454834   .1752972     0.83   0.407    -.1980928    .4890596
     Hispanic  |   .2251353   .1130965     1.99   0.047     .0034701    .4468004
        Asian  |   .1583555   .1770209     0.89   0.371    -.1885991    .5053101
American In..  |  -.1867431   .5609811    -0.33   0.739    -1.286246    .9127597
       Others  |   .0224363   .2461646     0.09   0.927    -.4600376    .5049101
Prefer not ..  |   .1915142   .3560459     0.54   0.591    -.5063229    .8893513
               |
           edu |
High school..  |  -.0163659   .2066893    -0.08   0.937    -.4214695    .3887377
 Some college  |  -.2020122   .2121982    -0.95   0.341    -.6179131    .2138887
 College grad  |  -.2185837   .2158967    -1.01   0.311    -.6417335    .2045661
    Post grad  |    .055673   .2254855     0.25   0.805    -.3862705    .4976165
        Other  |  -.7799531    .516034    -1.51   0.131    -1.791361     .231455
               |
      vote2016 |
      Clinton  |   .0136015   .0949461     0.14   0.886    -.1724894    .1996924
Other candi..  |   .0851748   .1798062     0.47   0.636    -.2672388    .4375884
      No vote  |  -.1524578    .110773    -1.38   0.169    -.3695689    .0646533
      Not say  |   .0770037   .2171422     0.35   0.723    -.3485871    .5025945
        Other  |   .4872084   .4779134     1.02   0.308    -.4494846    1.423901
               |
         _cons |  -.4175342    .262825    -1.59   0.112    -.9326616    .0975933
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Export Table A29 in Latex
. esttab  a3 a4 a5 a6 using "${main_appendix}/Table_A29.tex" ,  ///
>             b(3) star(* 0.10 ** 0.05  *** 0.01) se(3) label  ///
>                 title(Testing Hypothesis 3 and 4) replace       ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes(Note:Logit regression with heterscedasticity robus
> t standard errors.)
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Appendix/Table_A29.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Analysis with no deviations from pre-registration
. * Additional visualizations of the interaction effects
. * Figure A6: Response by subjects of opposing ideological outlooks
. * Figure A7: Preficted difference in probability that partisans will correctly 
> interpret the data
. * Figure A8: Predicted probabilities of correctly interpreting the data (2SD)
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A6: Response by subjects of opposing ideological outlooks
. *------------------------------------------------------------------------------
> -
. * No Incentives Treatment
. graph twoway    (lowess correct num if conservative<0 & treatment==1, bwidth(5)
>  adjust lcolor(blue) lpattern(solid) text(0.44 6.35 "COVID dec" "Congenial", co
> lor (blue) size(small)))  ///
>                                 (lowess correct num if conservative<0 & treatme
> nt==2, bwidth(5) adjust lcolor(blue) lpattern(dash)text(0.34 6.35 "COVID inc" "
> Uncongenial", color (blue) size(small)))  ///
>                                 (lowess correct num if conservative>0 & treatme
> nt==1, bwidth(5) adjust lcolor(red) lpattern(dash) text(0.51 6.35 "COVID dec" "
> Uncongenial", color (red) size(small)))   ///
>                                 (lowess correct num if conservative>0 & treatme
> nt==2, bwidth(5) adjust lcolor(red) lpattern(solid) text(0.58 6.35 "COVID inc" 
> "Congenial", color (red) size(small)))    ///
>                                 ,legend(position(6) cols (2) order(1 "" 2 "    
> Liberal Democrats" 3 "" 4 "    Conservative Republicans"))       ///
>                                 ylabel(0.2(0.2)0.8, nogrid) ytitle("Correct int
> erpretation of data (=1)")                               ///
>                                 xlabel(0(1)6.6) xtitle("Numeracy score")       
>  ///
>                                 title("Non-Incentivized Treatment") scheme(plot
> plain)

. graph export "${main_appendix}/Figure_A6_1.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A6_1.png saved as PNG format

. graph close

. 
. * Incentives Treatment
. graph twoway    (lowess correct num if conservative<0 & treatment==3, bwidth(5)
>  adjust lcolor(blue) lpattern(solid) text(0.53 6.35 "COVID dec" "Congenial", co
> lor (blue) size(small)))  ///
>                                 (lowess correct num if conservative<0 & treatme
> nt==4, bwidth(5) adjust lcolor(blue) lpattern(dash)text(0.33 6.35 "COVID inc" "
> Uncongenial", color (blue) size(small)))  ///
>                                 (lowess correct num if conservative>0 & treatme
> nt==3, bwidth(5) adjust lcolor(red) lpattern(dash) text(0.44 6.35 "COVID dec" "
> Uncongenial", color (red) size(small)))   ///
>                                 (lowess correct num if conservative>0 & treatme
> nt==4, bwidth(5) adjust lcolor(red) lpattern(solid) text(0.61 6.35 "COVID inc" 
> "Congenial", color (red) size(small)))    ///
>                                 ,legend(position(6) cols (2) order(1 "" 2 "    
> Liberal Democrats" 3 "" 4 "    Conservative Republicans"))       ///
>                                 ylabel(0.2(0.2)0.8) ytitle("Correct interpretat
> ion of data (=1)")                                               ///
>                                 xlabel(0(1)6.6) xtitle("Numeracy score")       
>  ///
>                                 title("Incentivized Treatment") scheme(plotplai
> n)

. graph export "${main_appendix}/Figure_A6_2.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A6_2.png saved as PNG format

. graph close

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A7: Predicted difference in probability that partisans will correctly 
> interpret the data
. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************
. *We generate the confidence intervals for Figure A7 using the following simulat
> ions that use the package Clarify. We use the data generated 
. *in these simulations to create the figure.
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 1*/
. /*CI below is for the no-incentives covid decreases (Treatment 1): low numeracy
> .*/
. /*For the simulation below: num=1 out 6 questions correctly solved, numeracy=-1
> .654, incentive =0*/
. /*Congenial = -1 for conservative and Congenial = +1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654 numsq_con 2.73
> 6 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5504388     .0313196      .487387    .6129417
             Pr(correct=1) |   .4495612     .0313196     .3870582     .512613

First Difference: congenial 1  -1 num_con -1.654 1.654 numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0352647     .0454657    -.1276779    .0560213

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 2*/
. /*CI below is for the no-incentives covid decreases (Treatment 1): high numerac
> y.*/
. /*For the simulation below: num=4.35 out 6 questions correctly solved, numeracy
> =+1.654, incentive =0*/
. /*Congenial = -1 for conservative and Congenial = +1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.73
> 6 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5081279     .0318749     .4406895    .5728944
             Pr(correct=1) |   .4918721     .0318749     .4271056    .5593105

First Difference: congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1517941     .0464921    -.2416572    -.056345

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 3*/
. /*CI below is for the no-incentives covid increases (Treatment 2): low numeracy
> .*/
. /*For the simulation below: num=1 out 6 questions correctly solved, numeracy=-1
> .654, incentive =0*/
. /*Congenial = +1 for conservative and Congenial = -1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 numsq_con -2.736 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial -1  1 num_con 1.654 -1.654 numsq_con -2.7
> 36 2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5857035     .0311671     .5223756    .6467589
             Pr(correct=1) |   .4142965     .0311671     .3532412    .4776244

First Difference: congenial -1  1 num_con 1.654 -1.654 numsq_con -2.736 2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0352647     .0454657    -.0560213    .1276779

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 4*/
. /*CI below is for the no-incentives covid increases (Treatment 2): high numerac
> y.*/
. /*For the simulation below: num=4.35 out 6 questions correctly solved, numeracy
> =1.654, incentive =0*/
. /*Congenial = +1 for conservative and Congenial = -1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 numsq_con -2.736 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial -1  1 num_con -1.654 1.654 numsq_con -2.7
> 36 2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .659922     .0311566       .59909    .7170123
             Pr(correct=1) |    .340078     .0311566     .2829877    .4009099

First Difference: congenial -1  1 num_con -1.654 1.654 numsq_con -2.736 2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .1517941     .0464921      .056345    .2416572

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 5*/
. /*CI below is for the incentives covid decreases (Treatment 3): low numeracy.*/
. /*For the simulation below: num=1 out 6 questions correctly solved, numeracy=-1
> .654, incentive =1*/
. /*Congenial = -1 for conservative and Congenial = +1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 1 in_con 1 in_num -1.654 in_numsq 2.736 in_num_con -1.654 in_numsq_con 2
> .736

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654 numsq_con 2.73
> 6 -2.736 in_con 1 -1 in_num_con -1.654 1.654 in_numsq_con 2.736 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6108749     .0218631     .5670119    .6513774
             Pr(correct=1) |   .3891251     .0218631     .3486226    .4329881

First Difference: congenial 1  -1 num_con -1.654 1.654 numsq_con 2.736 -2.736 in_
> con 1 -1 in_num_con -1.654 1.654 in_numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0106017     .0317074     -.054122    .0725858

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 6*/
. /*CI below is for the incentives covid decreases (Treatment 3): high numeracy.*
> /
. /*For the simulation below: num=4.35 out 6 questions correctly solved, numeracy
> =+1.654, incentive =1*/
. /*Congenial = -1 for conservative and Congenial = +1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 1 in_con 1 in_num 1.654 in_numsq 2.736 in_num_con 1.654 in_numsq_con 2.736

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.73
> 6 -2.736 in_con 1 -1 in_num_con 1.654 -1.654 in_numsq_con 2.736 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .505521     .0229586      .461436    .5496573
             Pr(correct=1) |    .494479     .0229586     .4503427     .538564

First Difference: congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.736 -2.736 in_
> con 1 -1 in_num_con 1.654 -1.654 in_numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0912489     .0314316    -.1503737   -.0238918

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 7*/
. /*CI below is for the incentives covid increases (Treatment 4): low numeracy.*/
. /*For the simulation below: num=1 out 6 questions correctly solved, numeracy=-1
> .654, incentive =1*/
. /*Congenial = +1 for conservative and Congenial = -1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 numsq_con -2.736 in
> centive 1 in_con -1 in_num -1.654 in_numsq 2.736 in_num_con 1.654 in_numsq_con 
> -2.736

. simqi, fd(prval(1)) changex(congenial -1  1 num_con 1.654 -1.654 numsq_con -2.7
> 36 2.736 in_con -1 1 in_num_con 1.654 -1.654 in_numsq_con -2.736 2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6002732     .0222593     .5566292    .6434962
             Pr(correct=1) |   .3997268     .0222593     .3565038    .4433709

First Difference: congenial -1  1 num_con 1.654 -1.654 numsq_con -2.736 2.736 in_
> con -1 1 in_num_con 1.654 -1.654 in_numsq_con -2.736 2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0106017     .0317074    -.0725858     .054122

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. /*Confidence Interval 8*/
. /*CI below is for the incentives covid increases (Treatment 4): high numeracy.*
> /
. /*For the simulation below: num=4.35 out 6 questions correctly solved, numeracy
> =1.654, incentive =1*/
. /*Congenial = +1 for conservative and Congenial = -1 for liberal*/
. /*We find the predicted differences in probability that partisans will correctl
> y interpret the data.*/
. /*Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)*/
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 numsq_con -2.736 in
> centive 1 in_con -1 in_num 1.654 in_numsq 2.736 in_num_con -1.654 in_numsq_con 
> -2.736

. simqi, fd(prval(1)) changex(congenial -1  1 num_con -1.654 1.654 numsq_con -2.7
> 36 2.736 in_con -1 1 in_num_con -1.654 1.654 in_numsq_con -2.736 2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5967699     .0218338     .5512834    .6375035
             Pr(correct=1) |   .4032301     .0218338     .3624965    .4487166

First Difference: congenial -1  1 num_con -1.654 1.654 numsq_con -2.736 2.736 in_
> con -1 1 in_num_con -1.654 1.654 in_numsq_con -2.736 2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0912489     .0314316     .0238918    .1503737

. drop b*

. 
. *******************************************************************************
> ****************************************
. *******************************************************************************
> ****************************************
. 
. use "${main_data}/Probdiff_data.dta", clear /*data in this file is generated us
> ing the simulations named Confidence interval 1-8 above*/

. set scheme plotplain

. graph twoway    (rcap ci_high ci_low row if prob_mean <= -0.05, horizontal lcol
> or(blue) lwidth(medium) yaxis(1)) ///
>                                 (rcap ci_high ci_low row if prob_mean >= 0.05, 
> horizontal lcolor(red) lwidth(medium) yaxis(1)) ///
>                                 (rcap ci_high ci_low row if prob_mean >= -0.05 
> & prob_mean <= 0.05, horizontal lcolor(black) lwidth(medium) yaxis(1)) ///
>                                 (rcap ci_high ci_low row if prob_mean <= -0.05,
>  horizontal lcolor(blue) lwidth(medium) yaxis(2)) ///
>                                 (rcap ci_high ci_low row if prob_mean >= 0.05, 
> horizontal lcolor(red) lwidth(medium) yaxis(2)) ///
>                                 (rcap ci_high ci_low row if prob_mean >= -0.05 
> & prob_mean <= 0.05, horizontal lcolor(black) lwidth(medium) yaxis(2)) ///
>                                 (scatter row prob_mean if prob_mean <= -0.05, m
> color(blue) msize(medlarge) msymbol(D)) ///
>                                 (scatter row prob_mean if prob_mean >= 0.05, mc
> olor(red)msize(medlarge) msymbol(D)) ///
>                                 (scatter row prob_mean if prob_mean >= -0.05 & 
> prob_mean <= 0.05, mcolor(black) msize(medlarge) msymbol(D)) ///
>                                 ,yscale(reverse) ///
>                                 yscale(axis(2) reverse) ///
>                                 ylabel(1 "No Incentive " 2 "COV decreases" 5 "N
> o Incentive " 6 "COV increases" 9 "Incentive    " 10 "COV decreases" 13 "Incent
> ive    " 14 "COV increases", angle(0) notick nogrid) ///
>                                 ylabel(1 "Low numeracy" 2 "High numeracy" 5 "Lo
> w numeracy" 6 "High numeracy" 9 "Low numeracy" 10 "High numeracy" 13 "Low numer
> acy" 14 "High numeracy", angle(0) axis(2) noticks) ///
>                                 ytitle("") ///
>                                 ytitle("", axis(2)) ///
>                                 xlabel(-0.25 "25%" -0.20 "20%" -0.15 "15%" -0.1
> 0 "10%" -0.05 "5%" 0 "0%" 0.05 "5%" 0.10 "10%" 0.15 "15%" 0.20 "20%" 0.25 "25%"
> , grid) ///
>                                 xtitle("Pct. difference in probability of corre
> ct interpretation of data") ///
>                                 xline(0, lcolor(gs8) lpattern(dash)) ///
>                                 legend(order(4 "Liberal Democrats more likely" 
> 6 "No difference between Lib-Dem vs Con-Rep" 5 "Conservative Republicans more l
> ikely") rows(3) position(6))

. graph export "${main_appendix}/Figure_A7.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A7.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> -
. * Reload data
. use "${main_data}/pol_v0.8.dta", clear
(Merges randomization data with pol_v0.5)

. *------------------------------------------------------------------------------
> -
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure A8: Predicted probabilities of correctly interpreting the data (2SD)
. *------------------------------------------------------------------------------
> -
. * The program "Clarify" is necessary to run these simulations.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. *------------------------------------------------------------------------------
> -
. * GRAPH5: TOP-LEFT Graph
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.654, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial -2 num_con 3.308 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .391411     .0495897      .302854    .4955317

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 2 num_con -3.308 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4754105     .0486562     .3802439    .5681036

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH5-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(6 0.26 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.58 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(large))                                                                 
>                                   ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%")                                                 
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("Low numeracy", size (large))            
>                                                                                
>                                                                   ///
>                                 name(topleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH6: TOP-RIGHT Graph
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=+1.654, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial -2 num_con -3.308 numsq 2.736 incentive 0 in_con 
> 0 in_num 0 in_num_con 0

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .280339     .0431102     .1975784     .365184

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 2 num_con 3.308 numsq 2.736 incentive 0 in_con 0 
> in_num 0 in_num_con 0

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .562722     .0487314     .4704762    .6486444

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH6-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(8 0.38 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(6 0.44 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%")                                                 
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("High numeracy", size (large))           
>                                                                                
>                                                           ///
>                                 name(topright2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH7: BOTTOM-LEFT Graph
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.654, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial -2 num_con 3.308 numsq 2.736 incentive 1 in_con 
> -2 in_num -1.654 in_num_con 3.308

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4100003     .0355205     .3436572    .4802149

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy -1.654 congenial 2 num_con -3.308 numsq 2.736 incentive 1 in_con 
> 2 in_num -1.654 in_num_con -3.308

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3802278     .0344066     .3156087    .4499954

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH7-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(7 0.53 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(7 0.25 "Congenial = +2", color (dkorange) size(small)))    /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("Incentivized", orientation(vertical) si
> ze(large))                                                                     
>                                           ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%")                                                 
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botleft2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH8: BOTTOM-RIGHT Graph
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs
. * High Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=+1.654, incentive =0
. 
. * Congenial = -2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial -2 num_con -3.308 numsq 2.736 incentive 1 in_con 
> -2 in_num 1.654 in_num_con -3.308

. simqi, prval(1) genpr(p4)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3545765     .0323268     .2945787    .4197758

Simqi generated the following new variable(s): p4

. drop b*

. 
. * Congenial = +2
. estsimp logit correct numeracy congenial num_con numsq incentive in_con in_num 
> in_num_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.7422
Iteration 2:   log pseudolikelihood =  -2060.735
Iteration 3:   log pseudolikelihood =  -2060.735

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(8)    =      31.32
                                                  Prob > chi2     =     0.0001
Log pseudolikelihood =  -2060.735                 Pseudo R2       =     0.0079

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0216887   .0390777    -0.56   0.579    -.0982796    .0549022
   congenial |   .1937113   .0651194     2.97   0.003     .0660795     .321343
     num_con |   .0651823   .0397025     1.64   0.101    -.0126333    .1429978
       numsq |   .0165881   .0126722     1.31   0.191     -.008249    .0414252
   incentive |  -.0049455   .0783168    -0.06   0.950    -.1584436    .1485527
      in_con |  -.1109787   .0794668    -1.40   0.163    -.2667306    .0447733
      in_num |   .0883382   .0475187     1.86   0.063    -.0047968    .1814732
  in_num_con |   .0030052   .0482509     0.06   0.950    -.0915648    .0975751
       _cons |  -.3595051   .0728584    -4.93   0.000    -.5023049   -.2167052
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 11% 22% 33% 44% 55% 66% 77% 88% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9

. setx numeracy 1.654 congenial 2 num_con 3.308 numsq 2.736 incentive 1 in_con 2 
> in_num 1.654 in_num_con 3.308

. simqi, prval(1) genpr(p5)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .5451644      .033653     .4786986     .613033

Simqi generated the following new variable(s): p5

. drop b*

. 
. *-------------------------------------------------------GRAPH8-----------------
> ------------------------------------------------
. graph twoway    (kdensity p4, lcolor(dknavy) lwidth(medthick) text(7 0.24 "Cong
> enial = -2", color (dknavy) size(small)))                ///
>                                 (kdensity p5, lcolor(dkorange) lwidth(medthick)
>  text(12 0.55 "Congenial = +2", color (dkorange) size(small)))   /// 
>                                 ,legend(off)                                   
>                                                                                
>                                                                                
>    ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>            ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 xlabel(0.1 "10%" 0.2 "20%" 0.3 "30%" 0.4 "40%" 
> 0.5 "50%" 0.6 "60%" 0.7 "70%")                                                 
>                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>            ///
>                                 title("")                                      
>                                                                                
>                                                                                
>            ///
>                                 name(botright2, replace) scheme(plotplain)

. graph close

. drop p4 p5 

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft2 topright2 botleft2 botright2, xcommon scheme(plotplain)

. graph export "${main_appendix}/Figure_A8.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Appendix/Figure_A8.png saved as PNG format

. graph close

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Analysis with no deviations from pre-registration
. * Difference in accuracy between supporters and opponents of mask mandates
. * Table A30: Difference in accuracy (high numeracy)
. * Table A31: Difference in accuracy (low numeracy)
. /*Table A30: Differences in accuracy between presumed supporters 
> and opponents of mask mandates (high numeracy respondents)*/    
. 
. su conservative, detail

         Standardized values of nonstd_conservative
-------------------------------------------------------------
      Percentiles      Smallest
 1%    -1.732688      -1.732688
 5%    -1.732688      -1.732688
10%    -1.431033      -1.732688       Obs               3,050
25%    -.8277222      -1.732688       Sum of wgt.       3,050

50%     .0772435                      Mean          -8.94e-09
                        Largest       Std. dev.             1
75%      .680554       1.887175
90%     1.283864       1.887175       Variance              1
95%     1.887175       1.887175       Skewness       .1424845
99%     1.887175       1.887175       Kurtosis        2.27534

. 
. *drop cons_dum
. gen cons_dum = 0

. replace cons_dum=1 if conservative>=1
(490 real changes made)

. tab cons_dum

   cons_dum |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,560       83.93       83.93
          1 |        490       16.07      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. *drop lib_dum
. gen lib_dum = 0

. replace lib_dum=1 if conservative<=-1
(571 real changes made)

. tab lib_dum

    lib_dum |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      2,479       81.28       81.28
          1 |        571       18.72      100.00
------------+-----------------------------------
      Total |      3,050      100.00

. 
. *** Conservative Republicans ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & num>=5 & cons_dum==1, by(covid_inc)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      12    .3333333    .1421338     .492366    .0204989    .6461677
       1 |      18    .7222222    .1086325    .4608886    .4930277    .9514167
---------+--------------------------------------------------------------------
Combined |      30    .5666667    .0920187    .5040069    .3784674    .7548659
---------+--------------------------------------------------------------------
    diff |           -.3888889    .1764646               -.7503603   -.0274175
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.2038
H0: diff = 0                                     Degrees of freedom =       28

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0180         Pr(|T| > |t|) = 0.0359          Pr(T > t) = 0.9820

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & num>=5 & cons_dum==1, by(covid_inc)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      30    .3333333    .0875376    .4794633    .1542988    .5123679
       1 |      27    .4814815    .0979908    .5091751    .2800585    .6829044
---------+--------------------------------------------------------------------
Combined |      57    .4035088    .0655593    .4949621    .2721777    .5348399
---------+--------------------------------------------------------------------
    diff |           -.1481481    .1309743               -.4106264    .1143301
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.1311
H0: diff = 0                                     Degrees of freedom =       55

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.1315         Pr(|T| > |t|) = 0.2629          Pr(T > t) = 0.8685

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Conservative, high num, no inc"  "Conservative, high num, in
> c"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

      ---------------------------------------------------------------------
                                        Congeniality less than 75th pct=0 
      ---------------------------------------------------------------------
       Conservative, high num, no inc                 0.33                
       Conservative, high num, inc                    0.33                
      ---------------------------------------------------------------------


---------------------------------------------------------------------------------
                                  Congeniality more than 75th pct=1  Difference 
---------------------------------------------------------------------------------
 Conservative, high num, no inc                 0.72                   -0.39    
 Conservative, high num, inc                    0.48                   -0.15    
---------------------------------------------------------------------------------


            --------------------------------------------------------
                                              t-statistic  p-value 
            --------------------------------------------------------
             Conservative, high num, no inc      -2.20      0.04   
             Conservative, high num, inc         -1.13      0.26   
            --------------------------------------------------------


.         
. *** ***DiD for High Numeracy Conservative Republicans: Unincentivzied vs. Incen
> tivized *** ***
. 
. *SD1=.1764646*(sqrt(30))=0.96653642021
. *SD2=0.1309743*(sqrt(57))=0.98883428027
. ttesti 30 -.3888889  0.96653642021     57 -.1481481    0.98883428027

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |      30   -.3888889    .1764646    .9665364   -.7497995   -.0279783
       y |      57   -.1481481    .1309743    .9888343   -.4105212     .114225
---------+--------------------------------------------------------------------
Combined |      87   -.2311622    .1053165    .9823272   -.4405245   -.0217998
---------+--------------------------------------------------------------------
    diff |           -.2407408    .2213381               -.6808202    .1993386
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =  -1.0877
H0: diff = 0                                     Degrees of freedom =       85

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.1399         Pr(|T| > |t|) = 0.2798          Pr(T > t) = 0.8601

. 
. *** Liberal Democrats ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & num>=5 & lib_dum==1, by(covid_dec)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      18    .2222222    .1008317    .4277926     .009486    .4349585
       1 |      19    .3684211    .1136972    .4955946    .1295521      .60729
---------+--------------------------------------------------------------------
Combined |      37    .2972973    .0761781    .4633732     .142801    .4517936
---------+--------------------------------------------------------------------
    diff |           -.1461988    .1525856               -.4559641    .1635665
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -0.9581
H0: diff = 0                                     Degrees of freedom =       35

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.1723         Pr(|T| > |t|) = 0.3446          Pr(T > t) = 0.8277

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & num>=5 & lib_dum==1, by(covid_dec)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      34    .3823529    .0845951    .4932702    .2102428    .5544631
       1 |      49    .6734694    .0676862    .4738035    .5373771    .8095617
---------+--------------------------------------------------------------------
Combined |      83    .5542169    .0548902    .5000735    .4450228    .6634109
---------+--------------------------------------------------------------------
    diff |           -.2911164    .1075461               -.5050995   -.0771334
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.7069
H0: diff = 0                                     Degrees of freedom =       81

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0041         Pr(|T| > |t|) = 0.0083          Pr(T > t) = 0.9959

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Liberal, high num, no inc"  "Liberal, high num, inc"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

        ----------------------------------------------------------------
                                     Congeniality less than 75th pct=0 
        ----------------------------------------------------------------
         Liberal, high num, no inc                 0.22                
         Liberal, high num, inc                    0.38                
        ----------------------------------------------------------------


  ----------------------------------------------------------------------------
                               Congeniality more than 75th pct=1  Difference 
  ----------------------------------------------------------------------------
   Liberal, high num, no inc                 0.37                   -0.15    
   Liberal, high num, inc                    0.67                   -0.29    
  ----------------------------------------------------------------------------


               ---------------------------------------------------
                                            t-statistic  p-value 
               ---------------------------------------------------
                Liberal, high num, no inc      -0.96      0.34   
                Liberal, high num, inc         -2.71      0.01   
               ---------------------------------------------------


. 
. *** ***DiD for High Numeracy Liberal Democrats: Unincentivzied vs. Incentivized
>  *** ***
. 
. *SD1=.1525856*(sqrt(37))=0.92814197034
. *SD2=.1075461*(sqrt(83))=0.97979160074
. ttesti 37       -.1461988 0.92814197034 83      -.2911164       0.97979160074

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |      37   -.1461988    .1525856     .928142   -.4556567    .1632591
       y |      83   -.2911164    .1075461    .9797916   -.5050599   -.0771729
---------+--------------------------------------------------------------------
Combined |     120   -.2464335    .0878744    .9626158   -.4204336   -.0724334
---------+--------------------------------------------------------------------
    diff |            .1449176     .190623               -.2325678     .522403
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   0.7602
H0: diff = 0                                     Degrees of freedom =      118

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7757         Pr(|T| > |t|) = 0.4486          Pr(T > t) = 0.2243

. 
. /*Table A31: Differences in accuracy between presumed supporters and 
> opponents of mask mandates (low numeracy respondents)*/ 
. 
. 
. *** Conservative Republicans ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & num<=1 & cons_dum==1, by(covid_inc)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      14    .2142857    .1138039    .4258153   -.0315727    .4601442
       1 |      21    .2857143    .1010153      .46291    .0750002    .4964284
---------+--------------------------------------------------------------------
Combined |      35    .2571429     .074955    .4434396     .104816    .4094697
---------+--------------------------------------------------------------------
    diff |           -.0714286    .1548035               -.3863787    .2435216
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -0.4614
H0: diff = 0                                     Degrees of freedom =       33

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.3238         Pr(|T| > |t|) = 0.6475          Pr(T > t) = 0.6762

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & num<=1 & cons_dum==1, by(covid_inc)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      46    .5434783    .0742533    .5036102    .3939245     .693032
       1 |      41    .3170732    .0735761     .471117    .1683703     .465776
---------+--------------------------------------------------------------------
Combined |      87    .4367816    .0534837    .4988626    .3304596    .5431037
---------+--------------------------------------------------------------------
    diff |            .2264051    .1049378                .0177606    .4350496
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   2.1575
H0: diff = 0                                     Degrees of freedom =       85

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9831         Pr(|T| > |t|) = 0.0338          Pr(T > t) = 0.0169

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Conservative, low num, no inc"  "Conservative, low num, inc"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

      --------------------------------------------------------------------
                                       Congeniality less than 75th pct=0 
      --------------------------------------------------------------------
       Conservative, low num, no inc                 0.21                
       Conservative, low num, inc                    0.54                
      --------------------------------------------------------------------


--------------------------------------------------------------------------------
                                 Congeniality more than 75th pct=1  Difference 
--------------------------------------------------------------------------------
 Conservative, low num, no inc                 0.29                   -0.07    
 Conservative, low num, inc                    0.32                    0.23    
--------------------------------------------------------------------------------


             -------------------------------------------------------
                                              t-statistic  p-value 
             -------------------------------------------------------
              Conservative, low num, no inc      -0.46      0.65   
              Conservative, low num, inc         2.16       0.03   
             -------------------------------------------------------


. 
. *** ***DiD for Low Numeracy Conservative Republicans: Unincentivzied vs. Incent
> ivized *** ***
. 
. *SD1=.1548035*(sqrt(35))=0.9158298567
. *SD2=.1049378*(sqrt(87))=0.97879463759
. ttesti 35  -.0714286    0.9158298567 87 .2264051 0.97879463759

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |      35   -.0714286    .1548035    .9158299   -.3860272      .24317
       y |      87    .2264051    .1049378    .9787946    .0177957    .4350145
---------+--------------------------------------------------------------------
Combined |     122     .140961    .0875391    .9669012   -.0323458    .3142678
---------+--------------------------------------------------------------------
    diff |           -.2978337    .1924325               -.6788366    .0831692
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =  -1.5477
H0: diff = 0                                     Degrees of freedom =      120

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0622         Pr(|T| > |t|) = 0.1243          Pr(T > t) = 0.9378

. 
. 
. *** Liberal Democrats ***
. mat T = J(2,5,.)

.          
. ttest correct if incentive==0 & num<=1 & lib_dum==1, by(covid_dec)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      26    .4615385    .0997037    .5083911    .2561948    .6668821
       1 |      24    .6666667    .0982946    .4815434    .4633287    .8700046
---------+--------------------------------------------------------------------
Combined |      50         .56    .0709124    .5014265    .4174962    .7025038
---------+--------------------------------------------------------------------
    diff |           -.2051282    .1403197               -.4872599    .0770035
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.4619
H0: diff = 0                                     Degrees of freedom =       48

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0751         Pr(|T| > |t|) = 0.1503          Pr(T > t) = 0.9249

. mat T[1,1] = r(mu_1)

. mat T[1,2] = r(mu_2)

. mat T[1,3] = r(mu_1) - r(mu_2)

. mat T[1,4] = r(t)

. mat T[1,5] = r(p)

. 
. ttest correct if incentive==1 & num<=1 & lib_dum==1, by(covid_dec)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       0 |      48        .375    .0706166    .4892461    .2329378    .5170622
       1 |      50         .52    .0713714     .504672    .3765738    .6634262
---------+--------------------------------------------------------------------
Combined |      98    .4489796    .0505023    .4999474    .3487465    .5492127
---------+--------------------------------------------------------------------
    diff |               -.145    .1004664               -.3444241    .0544241
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.4433
H0: diff = 0                                     Degrees of freedom =       96

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0761         Pr(|T| > |t|) = 0.1522          Pr(T > t) = 0.9239

. mat T[2,1] = r(mu_1)

. mat T[2,2] = r(mu_2)

. mat T[2,3] = r(mu_1) - r(mu_2)

. mat T[2,4] = r(t)

. mat T[2,5] = r(p)

. 
. mat rownames T =  "Liberal, low num, no inc"  "Liberal, low num, inc"

. 
.         frmttable using cp_ttest_table3a.doc, statmat(T) varlabels replace ///
>         ctitle("",  Congeniality less than 75th pct=0, Congeniality more than 7
> 5th pct=1, Difference, t-statistic, p-value)

         ---------------------------------------------------------------
                                     Congeniality less than 75th pct=0 
         ---------------------------------------------------------------
          Liberal, low num, no inc                 0.46                
          Liberal, low num, inc                    0.38                
         ---------------------------------------------------------------


   ---------------------------------------------------------------------------
                               Congeniality more than 75th pct=1  Difference 
   ---------------------------------------------------------------------------
    Liberal, low num, no inc                 0.67                   -0.21    
    Liberal, low num, inc                    0.52                   -0.15    
   ---------------------------------------------------------------------------


               --------------------------------------------------
                                           t-statistic  p-value 
               --------------------------------------------------
                Liberal, low num, no inc      -1.46      0.15   
                Liberal, low num, inc         -1.44      0.15   
               --------------------------------------------------


.         
.                 
. *** ***DiD for Low Numeracy Liberal Democrats: Unincentivzied vs. Incentivized 
> *** ***
. 
. *SD1=.1403197*(sqrt(50))=0.99221011404
. *SD2=.1004664*(sqrt(98))=0.9945666181
. ttesti  50      -.2051282  0.99221011404  98  -.145    .9945666181 

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |      50   -.2051282    .1403197    .9922101   -.4871112    .0768548
       y |      98       -.145    .1004664    .9945666    -.344398     .054398
---------+--------------------------------------------------------------------
Combined |     148   -.1653136    .0814434    .9908014   -.3262647   -.0043625
---------+--------------------------------------------------------------------
    diff |           -.0601282    .1727116                -.401466    .2812096
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =  -0.3481
H0: diff = 0                                     Degrees of freedom =      146

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.3641         Pr(|T| > |t|) = 0.7282          Pr(T > t) = 0.6359

. 
. 
. 
. 
. /**** Drop unnecessary dummies: ****/
. 
. drop cons_dum lib_dum

. 
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. log close
      name:  <unnamed>
       log:  /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/
> JEPSReplicationfiles/Appendix/appendixreplication_v2.log
  log type:  text
 closed on:  27 May 2022, 13:31:16
---------------------------------------------------------------------------------
